The diagram below shows part of the graph of the quadratic function f(x)=a(x-h)(x-k) with the condition h< k. point p is the minimum point for the graph of the quadratic function.
(a) calculate the values of
(i)h, (ii)k, (iii)a.
(b) determine the symmetry axis equation.
(c) state the coordinates of point p.

see explanation

Step-by-step explanation:

(a)

The zeros are x = 1 and x = 5, thus the factors are (x - 1) and (x - 5)

f(x) = a(x - 1)(x - 5)

To find a substitute (0, 15), the coordinates of the y- intercept into the equation.

15 = a(0 - 1)(0 - 5) = a(- 1)(- 5) = 5a ( divide both sides by 5)

a = 3

Thus h = 1, k = 5, a = 3 and

f(x) = 3(x - 1)(x - 5)

(b)

The axis of symmetry is a vertical line with equation x = c ( c is a constant )

The axis of symmetry passes through the midpoint of the zeros

x = = = 3

Equation of axis of symmetry is x = 3

(c)

The axis of symmetry passes through P, with x- coordinate x = 3

Substitute x = 3 into the function for corresponding value of y

f(3) = 3(3 - 1)(3 - 5) = 3(2)(- 2) = - 12

Coordinates of  P = (3, - 12 )

Step-by-step explanation:

hello : a=3 h=1 k=5

x=3 equation of symetric axis      P(3 ; -12)

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step-by-step explanation:

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