Expert: Sherman D. - 6/26/2009

Question
Write each quadratic function in standard quadratic form f(x) = a(x – h)2 + k .
Then state  (a) direction of opening … up or down
                  (b) x and y intercepts as ordered pairs
                  (c) coordinates of the vertex
                  (d) equation of the axis of symmetry (since these are functions,
                                                                             It will always be x =     )


1.   f(x) = x2 – 2x – 3

2.   f(x) = 4 – x2

3.   f(x) = x2 – 4x + 4


Answer
1.)
f(x) = x^2 - 2x - 3
f(x) = (x^2 - 2x) - 3
f(x) = (x^2 - 2x + 1 - 1) - 3
f(x) = (x^2 - 2x + 1) - 1 - 3
f(x) = (x - 1)^2 - 4

a.) Upward
b.) (0,-3), (3,0), and (-1,0)
c.) (1,-4)
d.) x = 1

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2.)
f(x) = 4 - x^2 or -x^2 + 4
f(x) = -(x - 0)^2 + 4

a.) Downward
b.) (0,4), (2,0), and (-2,0)
c.) (0,4)
d.) x = 0

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3.)
f(x) = x^2 - 4x + 4
f(x) = (x^2 - 4x) + 4
f(x) = (x^2 - 4x + 4 - 4) + 4
f(x) = (x - 2)^2 - 4 + 4
f(x) = (x - 2)^2

a.) Upward
b.) (0,4), no x-intercepts
c.) (2,0)
d.) x = 2

http://www.calculator.com/calcs/GCalc.html for graphs, but only type in what after the f(x) =, for ex: if you have f(x) = x^2, only type in the x^2 part, then click enter on the keyboard.