Question

Name Sometha Date 20 Kuta Software - Infinite Algebra 2 Properties of Parabolas Identify the vertex of each. 2) y = 2x² - 4x - 1) y = x² + 16x + 64 (3Question 1

Answer 1

Since the equation of the parabola is in standard form, then the x-coordinate of the vertex can be found like this:

`\begin{gathered} (-b)/(2a)\Rightarrow\text{ x-coordinate} \\ \text{ Where} \\ y=ax^2+bx+c \end{gathered}`

In this case, you have

`\begin{gathered} y=x^2+16x+64 \\ a=1 \\ b=16 \\ c=64 \end{gathered}`
`(-b)/(2a)=(-16)/(2\cdot1)=(-16)/(2)=-8\Rightarrow\text{ x-coordinate}`

Now that you have the x coordinate of the vertex, you can replace this value into the original equation of the parabola to find the y coordinate of the vertex:

`\begin{gathered} y=x^2+16x+64 \\ y=(-8)^2+16(-8)+64 \\ y=64-128+64 \\ y=0 \end{gathered}`

Therefore, the vertex of this parable is (-8,0).