Find an equation for the parabola with the given x-intercepts and y-intercept:

Question

x-intercepts (-1, 0) and (3, 0) and y-intercept at (0, -3)

Answer 1

axis of symmetry is x= 1 and vertex has an x coordinate of 1

axis of symmetry has an x value that is the midpoint between the 2 x intercepts (-1+3)/2 = 2/2 = 1

It's an upward opening parabola

general equation is

y= a(x-1)^2 + k, plug in the y intercept

-3 = a + k

plug in one of the x intercepts, (3,0)

0=a(3-1)^2 + k

0 =4a+k, subtract -3 = a+k to eliminate k

3=3a

a = 3/3 =1

-3 =a+k = 1+k

k =-4

y=(x-1)^2 -4 is the parabola with the given x and y intercepts