Given the quadratic function in standard form address the fo

Given the quadratic function in standard form, address the following f(x) = (x - 5)^2 - 9 What are the coordinates of the vertex? Does the graph \"open up\" or \"open down\"? What is the equation of the axis of symmetry?

Solution

f(x)=(x-6)²-9

This equation is of the form y=a(x-h)²+k

where vertex is (h,k)

And on comparing it with given equation we get

vertex =(6,-9)

since a is positive so it opens up

Axis of symmetry

For that we have to set the x term to zero

x-6=0

x=6 and that\'s the axis of symmetry

x intercepts

To find the x intercept we have to plug y=0

0=(x-6)²-9

9=(x-6)²

x-6=+-3

x=3,-9

Therefore the x intercepts are (3,0),(-9,0)

y intercepts

To find the y intercept we have to plug x =0

y= (0-6)²-9= 27

Therefore the y intercept is (0,27)