Answer:
the equation fits the situation, but the table doesn’t.
Step-by-step explanation:
For both functions, the lead roller coaster car starts at an initial height of 32 feet. This is the point (0,32), directly above Landon.
The car races past Landon’s field of vision (y = 0) after it moves a horizontal distance of 4 feet and then 8 feet with respect to the starting point. So, the correct function will have x-intercepts of 4 and 8.
Begin by checking the equation. Rewrite the equation in factored form:
f(x) =
− 11
+ 20x + 32
= (x + 1)(
− 12x + 32)
= (x + 1)(x − 4)(x − 8)
The equation has x-intercepts of 4 and 8.
But the table only has one x-intercept, located at (4,0). The point (8,160) is well out of Landon’s line of sight.
So, the equation fits the situation, but the table doesn’t.
Since these are parabolas with y being squared, the standard form of such a parabola with vertex at (h, k) is
<span>x = a(y - k)^2 + h </span>
<span>There are no steps. Just look at what is inside the parentheses and compare it to (y - k) with k = -3. </span>
<span>Then look at what is added and compare it to h = -1. </span>
<span>For instance, A has (y + 1) in parentheses. So k = -1. And it has -3 added, so h = -3. That would be a vertex at (-3, -1).</span>
You Answer Should Be D. For Every X There Should Be Only One Y
The slope is the change in Y over the change in X.
Slope = (0 - 1) / 4-2)
= -1/2
The slope is -1/2