Q: If $$f(x) = x^2$ - 5x - 9$$, what is the y-intercept of the graph?

$$f(0) = 0^2$ - 5 \times 0 - 9 = -9$$

Question 1

Given the function $$f(x) = x^2$ - 5x - 9$$, what is the value of $$f(5)$$?

Accepted Answer

$$f(5) = 25 - 25 - 9 = -9$$

Question 2

For the function $$f(x) = x^2$ - 5x - 9$$, what is $$f(x+3)$$?

Accepted Answer

$$f(x+3) = (x+3)^2$ - 5(x+3) - 9 = x^2$ + 6x + 9 - 5x - 15 - 9 = x^2$ + x - 15$$

Question 3

Evaluate $$f(-2x)$$ for $$f(x) = x^2$ - 5x - 9.$$

Accepted Answer

$$f(-2x) = (-2x)^2$ - 5(-2x) - 9 = 4x^2$ + 10x - 9$$

Question 4

If $$f(x) = x^2$ - 5x - 9$$, for which value of $$x$$ does $$f(x) = 0$$?

Accepted Answer

$$x = \dfrac{5 \pm \sqrt{25 + 36}}{2} = \dfrac{5 \pm 7.81}{2}$$

Question 5

A company models its profit with $$f(x) = x^2$ - 5x - 9$$, where $$x is $$the number of units sold (in thousands). If the company sells 8,000 units, what is its profit?

Accepted Answer

$$f(8) = 64 - 40 - 9 = 15$$

Question 6

Which of the following expressions correctly represents the difference $$f(x+3) - f(x)$$ for $$f(x) = x^2$ - 5x - 9$$?

Accepted Answer

$$f(x+3) - f(x) = (x^2$ + x - 15) - (x^2$ - 5x - 9) = 6x - 6$$

Question 7

Suppose $$f(x) = x^2$ - 5x - 9$$ models the height (in meters) of a projectile after $$x$$ seconds. At what time does the projectile reach its maximum height?

Accepted Answer

$$x = \dfrac{5}{2}$$

Question 8

Given $$f(x) = x^2$ - 5x - 9$$, what is the axis of symmetry of its graph?

Accepted Answer

$$x = \dfrac{5}{2}$$

Question 9

If $$f(x) = x^2$ - 5x - 9$$, what is the vertex of the parabola?

Accepted Answer

Vertex: $$\left( \dfrac{5}{2}, f\left( \dfrac{5}{2} \right) \right)$$

Question 10

For $$f(x) = x^2$ - 5x - 9$$, which transformation occurs when evaluating $$f(x+3)$$ compared to $$f(x)$$?

Accepted Answer

The graph shifts 3 units to the left.

Question 11

If $$f(x) = x^2$ - 5x - 9$$, what is the y-intercept of the graph?

Accepted Answer

$$f(0) = 0^2$ - 5 	imes 0 - 9 = -9$$

Question 12

A biologist models the population of a species with $$f(x) = x^2$ - 5x - 9$$, where $$x is $$the number of years since introduction. After how many years will the population be zero?

Accepted Answer

$$x = \dfrac{5 \pm \sqrt{25 + 36}}{2}$$

Question 13

For $$f(x) = x^2$ - 5x - 9$$, which of the following is the correct factored form?

Accepted Answer

$$f(x) = (x - \dfrac{5 + \sqrt{61}}{2})(x - \dfrac{5 - \sqrt{61}}{2})$$

Question 14

If $$f(x) = x^2$ - 5x - 9$$, what is the minimum value of $$f(x)$$?

Accepted Answer

The minimum value occurs at $$x = \dfrac{5}{2}$$ and is $$f\left( \dfrac{5}{2} ight) = \left( \dfrac{5}{2} \$$right)^2$$ - 5 	imes \dfrac{5}{2} - 9 = -15.25$$

Question 15

For $$f(x) = x^2$ - 5x - 9$$, which of the following describes the end behavior of the function?

Accepted Answer

As $$x 	o \infty$$, $$f(x) 	o \infty$$; as $$x 	o -\infty$$, $$f(x) 	o \infty$$

Question 16

A medical researcher uses $$f(x) = x^2$ - 5x - 9 to $$model the effectiveness of a drug over time, where $$x is $$the number of hours after administration. What is the rate of change of effectiveness at $$x = 4$$ hours?

Accepted Answer

The rate of change is $$f'(x) = 2x - 5$$, so at $$x = 4$$, $$f'(4) = 8 - 5 = 3$$

Question 17

If $$f(x) = x^2$ - 5x - 9$$, which of the following statements is true about the graph?

Accepted Answer

The parabola opens upwards and has a minimum point.

Question 18

For $$f(x) = x^2$ - 5x - 9$$, what is the sum of the roots of the equation $$f(x) = 0$$?

Accepted Answer

Sum of roots is $$5$$

Evaluating Functions and Function Notation in Precalculus

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