Question

Determine a and k so the given points are on the graph of the function.

Answer 1

Answer:

  y = -7(x +1)² +35

Step-by-step explanation:

The given quadratic equation has two parameters you are asked to find. When you fill in the given point values, the result is two linear equations in the two unknown parameters. You can solve these equations in any of the usual ways.

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equation for point (1, 7)

  y = a(x +1)² +k

  7 = a(1 +1)² +k

  7 = 4a +k

equation for point (2, -28)

  -28 = a(2 +1)² +k

  -28 = 9a +k

solution

The first equation can be subtracted from the second equation to eliminate the k variable. (This is solving by elimination.)

  (-28) -(7) = (9a +k) -(4a +k)

  -35 = 5a . . . . . . . . simplify

  -7 = a . . . . . . . . divide by 5

Using the first equation, we can find k.

  7 -4a = k . . . . . subtract 4a

  7 -4(-7) = k . . . . substitute for 'a'

  35 = k

The parameter values are a = -7, and k = 35. The quadratic equation is ...

  y = -7(x +1)² +35