Answer:
D: y = 3x² - 5x - 2
Explanation:
The general form of a quadratic equation is: y = ax² + bx + c
c is the y-intercept
We are given the point (0, -2) which is the y-intercept, so we can rewrite our general form into
y = ax² + bx - 2
We can create a system of equations to solve for a and b. We are given two points.
Equation 1: Take the first point (-2, 20) and plug it into our general equation...
20 = a(-2)² + b(-2) - 2
20 = 4a - 2b - 2
22 = 4a - 2b (add 2 to both sides)
11 = 2a - b (divide both sides by 2 since every coefficient is even)
Equation 2: Take the point (1, -4) and plug it into the general equation
-4 = a(1)² + b(1) - 2
-4 = a + b - 2
-2 = a + b
Now we have our 2 equations:
11 = 2a - b
-2 = a + b
Since the coefficients of b are already have opposite signs, add the two equations together (elimination method)
Now we have
9 = 3a now solve for a...
3 = a (divide by 3 on both sides)
If a = 3, then
-2 = 3 + b
-5 = b
Our equation is
y = 3x² - 5x - 2