Question

Mr. Walker gave his class the function f(x) = (x + 3)(x + 5). Four students made a claim about the function. Each student’s claim is below.
Jeremiah: The y-intercept is at (15, 0).
Lindsay: The x-intercepts are at (–3, 0) and (5, 0).
Stephen: The vertex is at (–4, –1).
Alexis: The midpoint between the x-intercepts is at (4, 0).
Which student’s claim about the function is correct?

Answer 1

Answer:

On E2020 its Stephen is correct

Step-by-step explanation:

Answer 2

Answer:

Stephen's claim is correct.

Step-by-step explanation:

The given function is

$f(x)=(x+3)(x+5)$

Put x=0 to find the y-intercepts.

$f(0)=(0+3)(0+5)=3\times 5=15$

The y-intercept of the function is at (0,15). It means jeremiah's statement is incorrect.

Put f(x)=0, to find the x-intercept.

$0=(x+3)(x+5)$

$x+3=0\Rightarrow x=-3$

$x+5=0\Rightarrow x=-5$

The x-intercepts are at (-3,0) and (-5,0). It means Lindsay's statement is incorrect.

$f(x)=(x+3)(x+5)$

$f(x)=x^2+8x+15$

$f(x)=x^2+8x+15+16-16$

$f(x)=(x^2+8x+16)-1$

$f(x)=(x+4)^2-1$                 .... (1)

The vertex form of a parabola is

$f(x)=(x-h)^2+k$                .... (2)

Where, (h,k) is vertex.

From (1) and (2) it is clear that the vertex of the parabola is (-4,-1), Stephen's claim is correct.

The midpoint between the x-intercepts is

$(\frac{-3-5}{2},\frac{0+0}{2})=(-4,0)$

The midpoint between the x-intercepts is at (-4, 0). It means Alexis's statement is incorrect.