Question

3) The graph of a quadratic function has the vertex (4, 2) and passes through the point (5,5). What

Answer 1

The equation of the function is:

$y = 3(x - 4)^2 + 2$

Solution:

The vertex form of equation is given as:

$y = a(x - h)^2 + k$

Where, (h, k) is the vertex

Given that, The graph of a quadratic function has the vertex (4, 2)

(h, k) = (4, 2)

Substitute in eqn

$y = a(x - 4)^2 + 2$

And passes through the point (5,5)

Substitute (x, y) = (5, 5) in above

$5 = a(5 - 4)^2 + 2\\\\5 = a + 2\\\\a = 3$

Substitute a = 3 and (h, k) = (4, 2) in vertex form

$y = 3(x - 4)^2 + 2$

Thus the equation of function is found