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)

options a,b,c are the right answer.

step-by-step explanation:

a linear parent function is always represented as y = x

if we write this function in the form of y=mx+c

⇒

or  

now if we plot a graph we will find these characteristics:

1) y intercept of the graph is zero so its a straight line passing through origin.

2) as we can see in both the forms of function written, values of x and y may be either positive or negative for the positive slope means points on the graph are either in first quadrant or in third one.

3) it's slope is one.