Question 1

Given the quadratic function $$f(x) = x^2$ + 6x + 5$$, what are the coordinates of the vertex?

Accepted Answer

$$(-3, -4)$$

Question 2

For the quadratic function $$y = -x^2$ + 2x - 7$$, what is the direction in which the parabola opens?

Accepted Answer

Downward

Question 3

What is the axis of symmetry for the function $$f(x) = (x-3)^2$ - 4$$?

Accepted Answer

$$x = 3$$

Question 4

A ball is thrown upward and its height in meters after $$t$$ seconds is modeled by $$h(t) = -5t^2$ + 20t + 2. At $$what time does the ball reach its maximum height?

Accepted Answer

$$t = 2$$

Question 5

Given $$f(x) = -3(x+2)^2$ + 3$$, what is the $$y-$$intercept?

Accepted Answer

$$y = -9$$

Question 6

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

Accepted Answer

$$f(x) = x^2$ - 4x + 12$$

Question 7

If a quadratic function has $$a \u003c 0$$, what does its graph look like?

Accepted Answer

It opens downward like $$\cap$$

Question 8

For $$f(x) = x^2$ + 6x + 5$$, what are the $$x-$$intercepts?

Accepted Answer

$$x = -1$$ and $$x = -5$$

Question 9

A company models its profit with $$P(x) = -2x^2$ + 8x + 10$$, where $$x is $$the number of units sold (in thousands). What is the maximum profit, and at how many units sold does it occur?

Accepted Answer

Maximum profit is $$18 at$$ $$x = 2$$

Question 10

Given $$f(x) = x^2$ + 6x + 5$$, what is the equation of the axis of symmetry?

Accepted Answer

$$x = -3$$

Question 11

Which of the following is the vertex form (H-K form) of $$y = x^2$ - 4x + 7$$?

Accepted Answer

$$y = (x-2)^2$ + 3$$

Question 12

For $$y = -x^2$ + 2x - 7$$, what is the $$y-$$intercept?

Accepted Answer

$$y = -7$$

Question 13

A satellite dish is shaped like a parabola described by $$y = 0.5(x-4)^2$ + 2. $$What is the minimum height of the dish?

Accepted Answer

$$2$$

Question 14

Given $$f(x) = (x-3)^2$ - 4$$, what are the $$x-$$intercepts?

Accepted Answer

$$x = 3 \pm 2$$

Question 15

If the vertex of a parabola is at $$(h, k)$$ and the equation is $$f(x) = a(x-h)^2$ + k$$, what is the axis of symmetry?

Accepted Answer

$$x = h$$

Question 16

A projectile is launched and its height is given by $$h(t) = -16t^2$ + 32t + 10. $$What is the maximum height reached by the projectile?

Accepted Answer

$$42$$

Question 17

For $$y = (x-2)^2$ + 8$$, what is the vertex?

Accepted Answer

$$(2, 8)$$

Question 18

Which of the following statements is true about the graph of $$y = -3(x+2)^2$ + 3$$?

Accepted Answer

The vertex is at $$(-2, 3)$$ and the parabola opens downward.

Question 19

If $$f(x) = ax^2$ + bx + c$$ and $$a \u003e 0$$, which of the following is always true?

Accepted Answer

The parabola opens upward.

Question 20

A bridge is designed in the shape of a parabola with equation $$y = -0.25(x-10)^2$ + 25. $$What is the maximum height of the bridge?

Accepted Answer

$$25$$

Step-by-Step Guidance for Quadratic Functions (Vertex, Intercepts, and Graphing)

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