SOLUTION: Consider the parabola: y=x^2-6x+5. (i) Complete the square. (ii) Give the Vertex. (iii) Give the x- and y-intercepts. (iv) Graph the parabola. I have been working on t

Click here to see ALL problems on Quadratic Equations

Question 34600: Consider the parabola: y=x^2-6x+5.
(i) Complete the square.
(ii) Give the Vertex.
(iii) Give the x- and y-intercepts.
(iv) Graph the parabola.
I have been working on this one but cannot get it right. Please help.
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
x^2-6x+5=y
(x^2-6x =y-5
Complete the square on the left side and maintain the equal sign, as follows;
x^2-6x+3^2 = y-5+3^2
Factor the left side and simplify the right side to get:
(x-3)^2 = y+4
a) The vertex is (3,-4)
b) To get the x-intercept, let y=0. Then
x^2-6x+5=0
(x-5)(x-1)=0
x=5 or x=1 (these are the x-intercepts
c) To get the y-intercept, let x=0
0^2-6(0)+5=y
y=5 This is the y intercept.
d) Graph as follows:

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=16 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 5, 1. Here's your graph: