Question

graph y= x² + 2x - 8. Then determine which answer choice matches the graph you drew. Find the x-intercepts.Identify the solution that has the correct graph and the correct x-intercepts.

Answer 1

ANSWER

Option A

EXPLANATION

First, we have to find the x-intercepts, so we have to solve,

$x^2+2x-8=0$

To do so, we can use the quadratic formula,

$\begin{gathered} ax^2+bx+c=0 \\ x=\frac{-b\pm\sqrt{b^2-4ac}}{2a} \end{gathered}$

In this case, a = 1, b = 2, and c = -8,

$x=\frac{-2\pm\sqrt{2^2-4\cdot1\cdot(-8)}}{2\cdot1}=\frac{-2\pm\sqrt{4+32}}{2}=\frac{-2\pm\sqrt{36}}{2}=\frac{-2\pm6}{2}$

So, the x-coordinates of the two x-intercepts are,

$\begin{gathered} x=\frac{-2-6}{2}=\frac{-8}{2}=-4 \\ \\ x=\frac{-2+6}{2}=\frac{4}{2}=2 \end{gathered}$

Hence, the x-intercepts are (-4, 0) and (2, 0), which reduces the graph options to two possibilities: graph A or graph C. Each has the x-coordinate of its vertex at each side of the y-axis: for graph A the x-coordinate of the vertex is negative, while for graph C it is positive.

To decide which one of these graphs is the correct one, we will find the x-coordinate of the vertex of the function, given by,

$x_{vertex}=\frac{-b}{2a}$

In this case, a = 1, and b = 2,

$x_{vertex}=\frac{-2}{2\cdot1}=-1$

Hence, the graph of this function is graph A.