Question 1

Given the quadratic function $$f(x) = 2x^2$ - 8x + 5$$, what are the coordinates of the vertex of its graph?

Accepted Answer

$$(2, -3)$$

Question 2

Which of the following best describes the direction in which the parabola $$f(x) = -3x^2$ + 6x - 1$$ opens?

Accepted Answer

Downward

Question 3

A ball is thrown upward from the ground and its height after $$t$$ seconds is given by $$h(t) = -4.9t^2$ + 19.6t. $$What is the maximum height reached by the ball?

Accepted Answer

Question 4

For the quadratic function $$f(x) = ax^2$ + bx + c$$, which formula gives the $$x-$$coordinate of the vertex?

Accepted Answer

$$x = -\frac{b}{2a}$$

Question 5

A company models its profit by $$P(x) = -2x^2$ + 12x - 16$$, where $$x is $$the number of items produced. What number of items maximizes the profit?

Accepted Answer

$$x = 4$$

Question 6

Which of the following is the vertex form of the quadratic function $$f(x) = x^2$ - 6x + 8$$?

Accepted Answer

$$f(x) = (x - 3)^2$ - 1$$

Question 7

If the vertex of the parabola $$f(x) = 5x^2$ + bx + c is at$$ $$(2, -7)$$, what is the value of $$b$$?

Accepted Answer

$$-20$$

Question 8

The graph of $$f(x) = 2(x - 1)^2$ + 3 is $$shifted compared to $$f(x) = x^2$. Which statement is true?

Accepted Answer

It is shifted right by 1 and up by 3.

Question 9

A parabola has its vertex at $$(5, -2)$$ and opens upward. Which could be its equation?

Accepted Answer

$$f(x) = (x - 5)^2$ - 2$$

Question 10

Which of the following statements is true about the graph of $$f(x) = -x^2$ + 4x - 1$$?

Accepted Answer

The vertex is a maximum point.

Question 11

A bridge is designed so that its arch follows the equation $$y = -0.5x^2$ + 3x + 2. $$What is the maximum height of the arch?

Accepted Answer

$$6.5$$ units

Question 12

Which of the following quadratic functions has its vertex at $$(0, 0)$$?

Accepted Answer

$$f(x) = x^2$

Question 13

If $$f(x) = 3x^2$ - 12x + 7$$, what is the minimum value of $$f(x)$$?

Accepted Answer

$$-5$$

Question 14

A quadratic function models the path of a projectile: $$h(t) = -16t^2$ + 32t + 5. $$How long after launch does the projectile reach its maximum height?

Accepted Answer

$$t = 1$$ seconds

Question 15

Which of the following is the axis of symmetry for the parabola $$f(x) = 4x^2$ - 8x + 1$$?

Accepted Answer

$$x = 1$$

Question 16

The profit $$P$$ from selling $$x$$ units is given by $$P(x) = -x^2$ + 10x - 16. $$What is the maximum profit?

Accepted Answer

$$34$$

Question 17

Which transformation occurs when the graph of $$f(x) = x^2$ is changed to f(x$$) = $$x^2 + 4$?

Accepted Answer

Shift upward by 4 units

Question 18

If $$f(x) = -2x^2$ + 8x - 3$$, what is the $$y-$$coordinate of the vertex?

Accepted Answer

$$5$$

Question 19

Which of the following is the standard form of a quadratic function?

Accepted Answer

$$f(x) = ax^2$ + bx + c$$

Question 20

A quadratic function $$f(x)$$ has its vertex at $$(3, 7)$$ and passes through the point $$(4, 10). $$Which is the value of $$a in$$ $$f(x) = a(x - 3)^2$ + 7$$?

Accepted Answer

$$1$$

Quadratic Functions and Their Graphs: Vertex Identification

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