Question

53

krissywatts
find the quadratic function y=ax^2+bx+c whose graph passes through the given points. (-1,14) (1,4) (3,2)

Answer 1

Recall that these point represent x and y-coordinate relationships on the curve. Since the curve passes through (-1,14) , we obtain that:

y = ax^2 + bx + c
==> 14 = a(-1)^2 + b(-1) + c
==> a - b + c = 14

Since it passes through (1,4)
we obtain:
y = ax^2 + bx + c
==> 4 = a(1)^2 + b(1) + c
==> a + b + c = 4

Then, it passes through (3,2) to get:

2 = a(3)^2 + b(3) + c
==> 9a + 3b + c = 2

Thus creating this system of equations:

{ a - b + c = 14
{ a + b + c = 4
{ 9a + 3b + c = 2

This system has solutions a = 1, b = -5, and c = 8.

Therefore, the quadratic function is y = x^2 - 5x + 8.
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Use the online calculator to solve 3 equations in 3 unknowns at the link:
http://www.analyzemath.com/Calculators/Calculator_syst_eq.html

Answer 2

Another approach to the solution is attached.