Question

+ 16x + 71 tion provided to write the vertex form equation of each parabola 2) y = x² - 2x - 5 y=ola-h2xmin Ye21XR125 Identify the vertex and axis of symmetry of each. Then sketch the graph. 15) f(x)=-3(x - 2)2 - 4 16) S(x)=-1)+4 po

Answer 1

Vertex

General equation of a parable

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

where

$(h,k)$

is the vertex

for our equation

$f(x)=-2(x+5)^2-2$

the vertex is

$(-5,-2)$

axis of symmetry

axis of symmetry is the x value of the vertex, then

$x=-5$

Graph

we replace values on x to find points of the parable

for example x=0

$\begin{gathered} f(0)=-2(0+5)^2-2 \\ f(0)=-2(5)^2-2 \\ f(0)=-2\times25-2 \\ f(0)=-50-2 \\ f(0)=-52 \end{gathered}$

x=-10

$\begin{gathered} f(-10)=-2(-10+5)^2-2 \\ f(-10)=-2(-5)^2-2 \\ f(-10)=-2\times25-2 \\ f(-10)=-50-2 \\ f(-10)=-52 \end{gathered}$

our three points

$\begin{gathered} (-5,-2) \\ (0,-52) \\ (-10,-52) \end{gathered}$