Answer:
c. (2, -4) and (-18, 36)
Explanation:
Step 1 - Simply the first equation and substitute the value of y into the second equation
y = 1/4x^2 + 2x - 9
y = x^2/ 4 + 2x - 9
x^2/ 4 + 2x - 9 = -x^2/ 4 - 6x + 9
Step 2 - Multiply both sides of the equation by four and move the terms to the left side
x^2/ 4 + 2x - 9 = -x^2/ 4 - 6x + 9
x^2/ 4 + 2x - 9 • 4/4 = -x^2/ 4 - 6x + 9 • 4/4
x^2 + 8x - 36 = -x^2 - 24x + 36
x^2 + 8x - 36 + x^2 + 24x - 36 = 0
Step 3 - Simplify & factor the common term
x^2 + 8x - 36 + x^2 + 24x - 36 = 0
2x^2 + 32x - 72 = 0
2(x^2 + 16x - 36) = 0
2(x - 2)(x + 18) = 0
x = 2, 18
Step 4 - Substitute x into the first equation and solve
y = x^2/4 + 2x - 9
y = 2^2/4 + 2 • 2 - 9, (-18)^2/4 + 2 • -18 - 9
y = -4, 36
Therefore, the points should be (2, -4) and (-18, 36).
