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

Answer:

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

Step-by-step 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

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