A quadratic function has its vertex at the point 5 9 The f

A quadratic function has its vertex at the point (- 5, - 9). The function passes through the point (2, 4). When written in vertex form, the function is f(x) = a(x - h)^2 + k, where: Box 1: Enter your answer as a number (like 5, -3, 2.2172) or as a calculation (like 5/3, 2^3, 5+4) Enter DNE for Does Not Exist, oo for Infinity Box 2: Enter your answer as a number (like 5, -3, 2.2172) or as a calculation (like 5/3, 2^3, 5+4) Enter DNE for Does Not Exist, or for

Solution

Given that function is f(x) = a(x-h)² +k

vertex (h, k) is at (-5, -9) and the function passes through the point (2, 4)

Substitute (h,k) = (-5, -9) and point (x, y) = (2,4) in given function.

f(x) = a(x-h)² +k

y = a(x-h)² +k

4 = a(4-(-5))² +(-9)

4 = a(4+5)² -9

4+9 = a (9)²

13 = 81a

a = 13/81

a = 0.1604

Therefore, function is  f(x) = (0.1604)(x-(-5))² -9

So, a = 0.1604

h = -5

k = -9