A Parabola has two x-intercepts. One is (4,0) and the other is unknown. The vertex is at (7,-3). Write the full equation in standard form

Question

Can someone please help me solve this.

Answer 1

If a parabola has 2 x-intercepts, it must be of the form

y - k = a (x - h)²

where (h,k) is the vertex. Since it is given that the vertex is (7,-3), we have that h = 7 and k = -3. So, the equation becomes

y + 3 = a (x - 7)²

For a, we use the fact that the parabola passes through point (4,0). Setting x = 4 and y = 0, we get

0 + 3 = a (4 - 7)²

3 = a (-3)²

3 = 9a

a = 1/3

Therefore, the equation of the parabola is

y + 3 = (1/3) (x - 7)²