3.1b Determining the Equation of a Quadratic Function
Review
Ex. Given the graphs below, determine its equation, axis of symmetry, domain and range,
whether it has a max/min, and any intercepts.
Equation:
Axis of Symmetry:
x-intercept(s):
Vertex:
y-intercept:
Domain:
Range:
Max/min:
Equation:
Axis of Symmetry:
x-intercept(s):
Vertex:
Domain:
Range:
y-intercept:
Max/min:
Ex. Determine the number of x-intercepts (think about "a" and the vertex...draw a quick sketch to help).
a) y = 0.9x2 - 5
b) y = -4(x + 2)2
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c) y = -¼(x - 2)2 - 3
In general, the number of x-intercepts depend on the value of a, and q.
 Two x-intercepts if parabola opens up and q is negative, or parabola opens down and q is positive.
 One x-intercept if q is zero.
 No x-intercepts if parabola opens up and q is positive, or parabola opens down and q is negative.
3.1b Determining the Equation of a Quadratic Function
Ex. Determine the equation of a parabola given:
a) vertex (3,-4) passing through (5,2)
b) vertex (-5, 2) with x-intercept 2
c)
Ex. Write the equation of each parabola.
a) With vertex (4, -1), that opens up, and is congruent to
y = 2x 2
b) With vertex (-2, 3), that opens down, and is congruent to y =
c) With the same vertex as the parabola,
but opens up.
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x2
y = 5(x - 7)2 - 9, the same shape as the parabola y = -4(x - 3)2,
Assignment: Sec. 3.1b p157 #6-9,21*
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