Question

question 28
write a function, f, whose zeros are -5, -2, and 0.
f(x)=x³+3x²−10x
f(x)=x³+7x²+10x
f(x)=x³−3x²−10x
f(x)=x³−7x²+10x
question 29
a rocket is launched. the rockets height, h (in feet), after t seconds is given by the equation below. what is the maximum height the rocket will reach?
h = 128t - 16t²
72 feet
80 feet
144 feet
256 feet

Explanation:

Question 28

Step1: Form factor from zeros

If $x=-5, x=-2, x=0$ are zeros, then $(x+5)$, $(x+2)$, and $x$ are factors.

Step2: Multiply factors to get function

$$f(x) = x(x+5)(x+2)$$

Step3: Expand the product

First multiply $(x+5)(x+2) = x^2 + 7x + 10$, then multiply by $x$:
$$f(x) = x(x^2 + 7x + 10) = x^3 + 7x^2 + 10x$$

Step1: Identify vertex of quadratic

For $h(t)=-16t^2+128t$, the vertex $t$-value is $t=-\frac{b}{2a}$ where $a=-16$, $b=128$.
<Expression>
$t = -\frac{128}{2(-16)} = \frac{128}{32} = 4$

Step2: Substitute t=4 into height function

<Expression>
$h(4) = 128(4) - 16(4)^2 = 512 - 16(16) = 512 - 256$

Answer:

B. $f(x)=x^3 + 7x^2 + 10x$

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Question 29