Question

Find the intersection of the parabola y=-x^2+2x+4 and the line 4x-y=-1

Answer 1

(-3, -11), (1, 5)

Step-by-step explanation

To solve this, we will solve this, we will equate the expressions for y

y = -x² + 2x + 4

4x - y = -1

y = 4x + 1

y = y

4x + 1 = -x² + 2x + 4

x² + 4x - 2x + 1 - 4 = 0

x² + 2x - 3 = 0

x² + 3x - x - 3 = 0

x (x + 3) - 1 (x + 3) = 0

(x + 3) (x - 1) = 0

x + 3 = 0

x = -3

OR

x - 1 = 0

x = 1

y = 4x + 1

If x = -3

y = 4x + 1 = 4(-3) + 1 = -12 + 1 = -11

If x = 1

y = 4x + 1 = 4(1) + 1 = 4 + 1 = 5

(-3, -11) OR (1, 5)

Hope this Helps!!!