A quadratic function goes through the points (−3, 3), (−1, 3), and (−2, 4). What is the axis of symmetry? Its vertex? Its equation?

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A quadratic function goes through the points (−3, 3), (−1, 3), and (−2, 4). What is the axis of symmetry? Its vertex? Its equation?

George Blue · Accepted Answer

Step 1 We know that general form of quadratic function 1) f(x)=ax2+bx+c vertex of the quadratic graph h=−b2a, k=f(h) (h, k) vertex ∵f(x) goes through (−3, 3), (−1, 3) and (−2, 4) then 2) 3=9a−3b+c 3) 3=a−b+c 4) 4=4a−2b+c Equation (2) - equation (3) 0=8a−2b ⇒8a=2b ⇒b=4a Putvalue of in equation (3) and (4) 3=a−4a+c=−3a+c 4=4a−8a+c=−4a+c 5) ∴3=−3a+c 6) 4=−4a+c Equation (5) - equation (6) 3−4=−3a+4a ⇒a=−1, b=−4 Value of a put in equation (5) 3=3+c⇒c=0 Hence f(x)=−x2−4x=−(x2+4x+(2)2−(2)2) ⇒f(x)=−(x+2)2+4 Vertex is: (−2, 4) axis of symmetry: x=−2

A quadratic function goes through the points (-3,\ 3),\ (-1,\

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