Write the standard form of the quadratic equation modeled by the points shown in the table below.
2 answers:
Answer:
y = 2x² - 5x + 7
Step-by-step explanation:
General form of a quadratic is:
y = Ax² + Bx + C
Using the given points, construct equations and solve for A,B and C.
When x = 0, y = 7
7 = A(0)² + B(0) + C
C = 7
y = Ax² + Bx + 7
When x = -1, y = 14
14 = A(-1)² + B(-1) + 7
A - B = 7
A = 7 + B
When x = 1, y = 4
4 = A(1)² + B(1) + 7
A + B = -3
(7 + B) + B = -3
2B = -10
B = -5
A = 7 + (-5)
A = 2
y = 2x² - 5x + 7
General form of a quadratic is:
y = Ax² + Bx + C
- Using the given points, construct equations and solve for A,B and C.
- When x = 0, y = 7
7 = A(0)² + B(0) + C
C = 7
y = Ax² + Bx + 7
When x = -1, y = 14
14 = A(-1)² + B(-1) + 7
A - B = 7
A = 7 + B
When x = 1, y = 4
4 = A(1)² + B(1) + 7
A + B = -3
(7 + B) + B = -3
2B = -10
B = -5
A = 7 + (-5)
A = 2
y = 2x² - 5x + 7
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