Question

State the y-intercept,x-intercepts,and vertex in point form.x2= is power of x to the 2 I can’t type 2 to the power on iOS Problem:Y=x2+2x-8

Answer 1

`\begin{gathered} \text{ y-intercept = }(0,-8) \\ x-\text{intercepts = }(2,0),(-4,0) \\ \text{vertex = }(-1,-9) \end{gathered}`

Explanation:

We have the following function:

`y=x^2+2x-8`

To calculate the y-intercept, the value of x must be 0, therefore:

`\begin{gathered} y=(0)^2+2\cdot0-8 \\ y=-8 \\ \text{ y-intercept = }(0,-8) \end{gathered}`

To calculate the x-intercept, the value of y must be 0, therefore:

`\begin{gathered} 0=x^2+2x-8 \\ (x-2)\cdot(x+4)=0 \\ x-2=0\rightarrow x=2 \\ x+2=0\rightarrow x=-4 \\ x-\text{intercepts = }(2,0),(-4,0) \end{gathered}`

In the case of the vertex, we calculate it as follows:

`\begin{gathered} x_v=-(b)/(2a) \\ a=1 \\ b=2 \\ \text{ replacing:} \\ x_v=-(2)/(2\cdot1)=-1 \\ \text{ now, we calculate y, replacing:} \\ y_v=(-1)^2+2\cdot(-1)-8 \\ y_v=1-2-8 \\ y_v=-9 \\ \text{therefore:} \\ \text{vertex = }(-1,-9) \end{gathered}`