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Quizzes > High School Quizzes > Mathematics

Edgenuity Quadratic Functions Practice Quiz

Sharpen your skills with clear quiz answers

Difficulty: Moderate
Grade: Grade 9
Study OutcomesCheat Sheet
Colorful paper art promoting Quadratic Kickstart Quiz for high school students.

Which of the following is the standard form of a quadratic equation?
ax^3 + bx + c = 0
ax^2 + bx + c = 0
a + bx^2 + cx = 0
ax + b = 0
The standard form of a quadratic equation is written as ax^2 + bx + c = 0, where a, b, and c represent constants and a 0. This format clearly highlights the quadratic term.
In the quadratic function f(x) = 3x^2 - 6x + 2, what is the value of 'a'?
3
-6
2
1
In a quadratic function written as f(x) = ax^2 + bx + c, the coefficient 'a' is the multiplier of x^2. Here, a equals 3, making it the correct choice.
What is the vertex form of a quadratic function?
f(x) = (x + p)(x + q)
f(x) = a(x - h)^2 + k
f(x) = a(x + h)^2 + k
f(x) = ax^2 + bx + c
The vertex form of a quadratic function is given by f(x) = a(x - h)^2 + k, where (h, k) represents the vertex. This form makes it straightforward to identify horizontal and vertical shifts.
How many solutions can a quadratic equation have?
Exactly 0
Up to 3
Exactly 1
Up to 2
A quadratic equation can have 0, 1, or 2 real solutions depending on the discriminant. The maximum number of solutions is 2, making this the correct answer.
What method is used to solve a quadratic equation by rewriting it as a product of two binomials?
Factoring
Graphing
Completing the square
Using the quadratic formula
Factoring is a method where a quadratic equation is rewritten as a product of two binomials. This allows each factor to be set equal to zero to solve for x.
For the quadratic equation x^2 - 4x + 3 = 0, which of the following represents its factored form?
(x + 1)(x + 3)
(x - 2)(x - 2)
(x + 1)(x - 3)
(x - 1)(x - 3)
The quadratic x^2 - 4x + 3 factors into (x - 1)(x - 3), as expanding these binomials returns the original equation. This shows the roots x = 1 and x = 3.
What does the discriminant of a quadratic equation provide information about?
The vertex of the parabola
The number and type of solutions
The y-intercept
The axis of symmetry
The discriminant, calculated as b^2 - 4ac, indicates whether the quadratic equation has two real solutions, one real solution, or two complex solutions. It provides direct insight into the nature of the roots.
Which method completes the square on the quadratic equation x^2 + 6x + 5 = 0?
Use the quadratic formula directly
Divide the equation by x
Rewrite as (x + 3)^2 - 4 = 0
Factor into (x + 1)(x + 5) = 0
Completing the square transforms x^2 + 6x into (x + 3)^2 by adding and subtracting 9, then adjusting the constant term to form (x + 3)^2 - 4 = 0. This method isolates the perfect square for easier solution extraction.
What is the axis of symmetry for the quadratic function f(x) = 2x^2 - 8x + 3?
x = -4
x = 4
x = 2
x = -2
The axis of symmetry of a quadratic function is determined using the formula x = -b/(2a). For f(x) = 2x^2 - 8x + 3, this calculation results in x = 2, which is the correct axis.
For the quadratic function f(x) = -(x - 1)^2 + 4, what is the vertex?
(1, 4)
(1, -4)
(-1, -4)
(-1, 4)
In the vertex form f(x) = a(x - h)^2 + k, the vertex is (h, k). In the equation f(x) = -(x - 1)^2 + 4, the vertex is clearly (1, 4).
How do you determine if a quadratic function opens upwards or downwards?
Check the sign of the coefficient a
Identify the vertex's x-coordinate
Look at the value of c
Use the discriminant
The sign of the coefficient a in the quadratic function f(x) = ax^2 + bx + c decides the opening direction. A positive a means the parabola opens upward and a negative a means it opens downward.
Solve the quadratic equation 2x^2 + 3x - 2 = 0 using the quadratic formula. Which is one of its solutions?
x = -0.5
x = 2
x = 0.5
x = -2
Applying the quadratic formula to 2x^2 + 3x - 2 = 0 yields discriminant 25, and one solution simplifies to x = 0.5. This is one of the two valid solutions.
Which of the following quadratic equations has no real solutions?
x^2 + 2x + 1 = 0
x^2 + 4x + 8 = 0
x^2 - 2x - 3 = 0
x^2 - 4x + 3 = 0
The equation x^2 + 4x + 8 = 0 has a discriminant that is negative, indicating that the solutions are complex rather than real. This is a key indicator of no real solutions.
What is the effect of a negative coefficient 'a' in the quadratic function f(x) = ax^2 + bx + c?
The vertex is at the origin
The parabola opens downward
The parabola opens upward
The function has no axis of symmetry
A negative 'a' in the quadratic function causes the parabola to open downward. This inversion alters the maximum and minimum values of the function.
How do you find the vertex of a quadratic function given by f(x) = x^2 + 6x + 5?
Use -b/(2a) to find x, then calculate f(x)
Set x equal to 0
Use the discriminant
Factor the quadratic
To locate the vertex, first compute the x-coordinate using the formula -b/(2a), and then substitute back into the function to obtain the y-coordinate. This method reliably identifies the vertex for any quadratic function.
Given the quadratic function f(x) = 2x^2 - 12x + 16, determine the coordinates of the vertex by completing the square.
(6, 2)
(6, -2)
(3, -2)
(3, 2)
By completing the square, f(x) is rewritten in vertex form as 2(x - 3)^2 - 2. This conversion shows that the vertex of the parabola is located at (3, -2).
Determine the axis of symmetry for the quadratic function f(x) = -3x^2 + 18x - 24 using the vertex formula.
x = -3
x = 6
x = -6
x = 3
Using the formula x = -b/(2a) for the axis of symmetry, substituting a = -3 and b = 18 results in x = 3. This vertical line is the correct axis that divides the parabola equally.
Find the value of 'k' for which the quadratic equation x^2 + 4x + k = 0 has exactly one real solution.
2
0
4
-4
A quadratic equation has exactly one real solution when its discriminant is zero. For the equation x^2 + 4x + k = 0, setting the discriminant (16 - 4k) to zero gives k = 4.
If the vertex of the quadratic function f(x) = ax^2 + bx + c is (2, 5) and it passes through the point (4, 13), what is the value of 'a'?
3
-2
2
4
Expressing the function in vertex form as f(x) = a(x - 2)^2 + 5 and substituting x = 4 gives 13 = a(2)^2 + 5, which simplifies to 4a = 8, so a equals 2. This method uses the vertex and a known point to determine a.
Which transformation of the quadratic function f(x) = x^2 results in a parabola that is reflected over the x-axis and shifted upward by 3 units?
f(x) = -x^2 - 3
f(x) = x^2 + 3
f(x) = -x^2 + 3
f(x) = -x^2
Reflecting the graph over the x-axis requires changing the sign of the quadratic term, and shifting upward involves adding a positive constant. Therefore, f(x) = -x^2 + 3 correctly represents both transformations.
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Study Outcomes

  1. Analyze quadratic equations to determine their components and properties.
  2. Evaluate and solve quadratic functions using factoring and the quadratic formula.
  3. Interpret the shape and features of quadratic graphs, including vertex and axis of symmetry.
  4. Apply problem-solving techniques to real-world scenarios involving quadratic functions.
  5. Synthesize learned concepts to pinpoint areas for further improvement in quadratic equations and functions.

Edgenuity: Intro to Quadratic Functions Cheat Sheet

  1. Understand the Standard Form - Every quadratic shows off its style with f(x)=ax²+bx+c, where a, b, and c define shape and position. Master this form to quickly sketch parabolas and predict their shifts. OpenStax - Precalculus: Quadratic Functions
  2. Parabola Direction - A parabola smiles upward when a > 0 and frowns downward when a < 0, so checking the sign of a tells you which way it opens. This little trick lets you read the curve's mood at a glance! OpenStax - Precalculus: Quadratic Functions
  3. Find the Vertex - Use h = -b/(2a) to nail the x-coordinate of the vertex, then plug it back in to get the y-coordinate. The vertex is your parabola's highest or lowest hangout spot! OpenStax - Precalculus: Quadratic Functions
  4. Axis of Symmetry - Parabolas are mirror images split by the line x = h (where h is the vertex's x-value). This symmetry line gives you a roadmap for plotting matching points on both sides. OpenStax - Precalculus: Quadratic Functions
  5. Quadratic Formula - Break out the boss formula x = (-b ± √(b² - 4ac))❄(2a) to solve any quadratic like a champ. No more factoring headaches - this tool handles every case! Symbolab - Quadratic Functions
  6. Discriminant Magic - The discriminant D = b² - 4ac reveals whether your roots are two real buddies (D > 0), a lone double root (D = 0), or a pair of complex twins (D < 0). Knowing D's value is like having cheat codes for root types! Symbolab - Quadratic Functions
  7. Factoring Fun - Turn x² - 5x + 6 into (x - 2)(x - 3) = 0 to score roots x=2 and x=3 in record time. Factoring is your quick-draw method when the numbers play nice! SparkNotes - Quadratics Study Guide
  8. Vertex Form - Write f(x)=a(x - h)² + k to spotlight the vertex (h, k) and see shifts straightaway. This form is your graphing shortcut for translations and stretches. Symbolab - Quadratic Functions
  9. Transformations - Vertical shifts add or subtract k to move your curve up/down, horizontal shifts change h to slide it left/right, and tweaking a stretches or squishes the parabola. Mix these moves to create custom parabolas in no time! Symbolab - Quadratic Functions
  10. Real-World Practice - Apply quadratics to projectile motion or area optimization problems to see math jump off the textbook. Real-life scenarios make your skills stick and show you why parabolas matter! Pearson - Quadratic Functions
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