Find the point(s) of intersection of the parabola with equation y = x^2 - 5x + 4 and the line with equation y = 2x - 2

Expert Answers

An illustration of the letter 'A' in a speech bubbles

At the point of intersection of the parabola y = x^2 - 5x + 4 and the line y = 2x - 2, the value of x and y is equal.

So we can equate the two and solve for x.

x^2 - 5x + 4 = 2x - 2

=> x^2 - 7x + 6 = 0

=> x^2 - 6x - x + 6 = 0

=> x(x-6) - 1(x - 6) = 0

=> (x - 1)(x -6) = 0

So we have x = 1 and 6

The value of y for x = 1 is 0 and for x = 6, y = 10.

Therefore the point of intersection are ( 1, 0) and (6, 10)

Approved by eNotes Editorial Team

Posted on

An illustration of the letter 'A' in a speech bubbles

Given the parabola y= x^2 - 5x + 4 and the line y= 2x-2

We need to find the intersection points of the parabola and the line.

The intersection points are the values of x and y such that:

the parabola y = the line y

==> x^2 - 5x + 4 = 2x -2

We will combine like terms and solve for x.

==> x^2 - 7x + 6 = 0

Now we will factor.

==> (x-6)(x-1) = 0

==> x1= 6  ==> y1= 2*6-2 = 10

==> x2 = 1==> y2= 2*1 -2 = 0

Then we have two intersection points:

The intersection points of the parabola and the line are (6, 10) and (1,0)

Approved by eNotes Editorial Team

Posted on

Soaring plane image

We’ll help your grades soar

Start your 48-hour free trial and unlock all the summaries, Q&A, and analyses you need to get better grades now.

  • 30,000+ book summaries
  • 20% study tools discount
  • Ad-free content
  • PDF downloads
  • 300,000+ answers
  • 5-star customer support
Start your 48-Hour Free Trial