Question

given three points of a quadratic function find the equation that defines the function (-2,20)(0,-2)(1,-4) hurry please!!​

Answer 1

Answer:

D: y = 3x² - 5x - 2

Step-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 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