Question

The equation of the parabola with vertex (-5,3), with axis parallel to the x-axis, opening to the right and with x-intercept x = 4 is___________.

Answer 1

`x=1(y-3)^2-5`

Explanation:

we need to find the equation of the parabola with vertex (-5,3), with axis parallel to the x-axis.

general equation of horizontal parabola is

`x=a(y-k)^2+h`

where (h,k) is the vertex

(-5,3) is the vertex. h=-5 and k=3. plug in the values in the general equation

`x=a(y-3)^2-5`

Now find out the value of 'a' using x intercept (4,0)

`4=a(0-3)^2-5`

`4=a(-3)^2-5`

`4=9a-5`

Add 5 on both sides

`9=9a`

a=1

the equation becomes

`x=1(y-3)^2-5`