Question

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.​

Answer 1

Answer:

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 = $\frac{1+5}{2}$ = $\frac{6}{2}$ = 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 )

Answer 2

Answer:

Step-by-step explanation:

hello : a=3 h=1 k=5

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