Question

Write a quadratic function in vertex form for the function whose graph has it's vertex at (5,4) and passes through the point (7,1)a quadratic function

Answer 1

y = - $\frac{3}{4}$ (x - 5)² + 4

the equation of a quadratic in standard form is

y = a(x - h)² + k ( where (h , k ) are the coordinates of the vertex and a is a multiplier )

given vertex = ( 5, 4 ) then

y = a(x - 5)² + 4 ( to find a substitute (7 , 1 ) into the equation )

1= 4a + 4

4a = - 3 ⇒ a = - $\frac{3}{4}$

y = - $\frac{3}{4}$ (x - 5)² + 4 ← ( in vertex form )