Find the coordinate of the point of intersection of the parabola?

Question

y= -x²+9x-3 and the line y=3x
I got the anwser 3+/- √9, but how do I apply this to the equations?

Show/explain please.

Answer 1

Find the point(s) of intersection.

y= -x² + 9x - 3
y = 3x

Set the equations equal to each other.

y= -x² + 9x - 3 = 3x
-x² + 6x - 3 = 0

x = {-6 ± √[36 - 4(-1)(-3)]} / [2(-1)]
x = (-6 ± √24) / (-2)
x = (6 ± 2√6) / 2
x = 3 ± √6

Now plug these values back into one of the equations to solve for y. Let's use y = 3x. It's easier.

y = 3*[3 ± √6] = 9 ± 3√6

The points of intersection are:

(3 + √6, 9 + 3√6) and (3 - √6, 9 - 3√6)

Answer 2

Plug them in for x into either equation and evaluate y. I suggest using the line...it's easier. Remember to evaluate both points and express the answers as ordered pairs (x, y).