Question 1

Which method is most appropriate for solving the quadratic equation $$x^2 + 7x + 12 = 0$?

Accepted Answer

By factoring

Question 2

A projectile is launched from ground level with an initial velocity of $$v_0 = 20$ m/s. Its height h$ after t$ seconds is given by h$$ = $$-5t^2 + 20t$. What is the maximum height reached by the projectile?

Accepted Answer

$$15 m$$

Question 3

Solve for $$x$$: $$x^2 - x - 6 = 0$

Accepted Answer

$$x = 3 or$$ $$x = -2$$

Question 4

Given $$f(x) = x - 3$$ and $$g(x) = -2x + 6$$, what is $$f(g(2))$$?

Accepted Answer

$$-7$$

Question 5

If $$f(x) = x^2$ + 5x - 2$$, what are the roots of $$f(x)$$ using the quadratic formula?

Accepted Answer

$$x = \frac{-5 \pm \sqrt{33}}{2}$$

Question 6

Which of the following is the correct difference quotient for $$f(x) = x^2$?

Accepted Answer

$$\frac{f(x+h) - f(x)}{h} = \frac{(x+h)^2$ - x^2$}{h}$$

Question 7

If $$f(x) = x^2$ - 5x + 6$$, what are the factors of $$f(x)$$?

Accepted Answer

$$(x - 2)(x - 3)$$

Question 8

A student solves $$x^2 + 5x - 2 = 0$ by factoring and gets x = -5$ and x = 2$. What mistake did the student make?

Accepted Answer

Factoring was not possible; the quadratic formula should be used.

Question 9

Given $$f(x) = x^2$ - 5x + 6$$, what is $$f(2)$$?

Accepted Answer

$$0$$

Question 10

If $$g(x) = -2x + 6$$, what is $$g(f(1))$$ where $$f(x) = x - 3$$?

Accepted Answer

$$2$$

Question 11

What is the value of $$f(3)$$ for $$f(x) = x^2$ - 5x + 6$$?

Accepted Answer

$$0$$

Question 12

Which of the following is the correct quadratic formula?

Accepted Answer

$$x = \frac{-b \pm \sqrt{b^2$ - 4ac}}{2a}$$

Question 13

If $$f(x) = x^2$ - 5x + 6$$, what is the sum of the roots?

Accepted Answer

$$5$$

Question 14

A ball is thrown upward from the ground with an initial velocity of $$v_0 = 20$ m/s. How long does it take to reach its maximum height?

Accepted Answer

$$2$$ seconds

Question 15

What is the value of $$f(0)$$ for $$f(x) = x^2$ - 5x + 6$$?

Accepted Answer

$$6$$

Question 16

Which of the following represents the composition $$f(g(x))$$ for $$f(x) = x - 3$$ and $$g(x) = -2x + 6$$?

Accepted Answer

Question 17

If $$f(x) = x^2$ - 5x + 6$$, what is the product of the roots?

Accepted Answer

$$6$$

Question 18

Which of the following is the correct factorization for $$x^2 + 5x - 2$?

Accepted Answer

Cannot be factored with integer roots

Question 19

If $$f(x) = x^2$ - 5x + 6$$, what is $$f(-1)$$?

Accepted Answer

$$12$$

Precalculus Test 1 Practice – Step-by-Step Study Guidance

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