given three points of a quadratic function find the equation that defines the function (-2,20)(0,-2)(1,-4) hurry please!!
Accepted Solution
A:
Answer:D: y = 3x² - 5x - 2Step-by-step 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 intoy = ax² + bx - 2We 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 + bNow we have our 2 equations:11 = 2a - b-2 = a + bSince the coefficients of b are already have opposite signs, add the two equations together (elimination method)Now we have9 = 3a now solve for a... 3 = a (divide by 3 on both sides)If a = 3, then -2 = 3 + b -5 = bOur equation is y = 3x² - 5x - 2