Use quadratic regression to find the equation of the parabola going through these 3 points.

Question

(-3,88), (2,-27), (4,-17)

y= 4x2-19x+?

Answer 1

y = 4x
2 + 19x − 5
You can factor the right-hand side by using the "splitting the middle term" method.
Multiply the coefficient of the rst term by the constant.
4 × − 5 = − 20
Find two numbers that when added equal −19, which is the coefcient of the middle term, and that multiply to −20. The numbers 20 and −1 meet the
requirements.
Split 19x as the sum of 20x and −x.
y = 4x
2 + 20x − x − 5
Factor out the common terms in the rst two terms and the second two terms.
y = 4x(x + 5) − (x + 5)
It is understood that −(x + 5) is −1(x + 5).
Factor out the common term x + 5.
y = (x + 5)(4x − 1)

Answer 2

using your three points, you get
88 = 36+57+?
? = -4

-27 = 8-38+?
? = -3

-17 = 64-76+?
? = -5

so, what do you think?