Finding quadratic in general form using vertex and two x intercepts.

Question

Find the quadratic (in general form) that passes through these 3 points. The three points are the vertex, and two x intercepts. The vertex is (55, 24) and the two x intercepts are (0, 0) and (0, 110).

Answer 1

We can set up this equation in its factored form using the x intercepts.

y=a(x-0)(x-110) and simplified

y=a(x)(x-110)

To figure out what a is, the vertical stretch which will give us the vertex at (55,24), we can plug in the vertex as the x and y coordinates and solve for a

24 = a(55)(55-110)

24 = -3025a

Divide both sides by -3025

24/-3025 = -3025a/-3025

This simplifies to

a=-24/3025

The equation is y=-24/3025x(x-110)

We can use the distributive property to get general form

y=-24/3025x²+48/55x