Question

Find a quadratic function f(x)=ax^2+bx+c for the parabola with minimum value -5 and x-intercepts -3 and 7??

Answer 1

You have to input the minimum value and the x,y coordinates into the vertex form of a parabola.
Then convert the vertex form to standard form .

Answer 2

ok thank you so much! @sophiav95

Answer 3

a really easy solution is to recognize the line of symmetry is halfway between the intercepts... and the vertex lies on the line of symmetry

(-3 + 7)/2 = 2

so the line of symmetry is x = -2 you know the min value y = -5

so the vertex is

(-2, -5)

so then substitute the point into the vertex from of the parabola

\[y = (x - h)^2 + k\]

where (h, k) is the vertex