Write an equation of a parabola that satisfies each set of conditions.a) opens upward, congruent with y = 2x', vertex (4, –1)b) opens downward, congruent with y =vertex (-2, 3)%3Dc) opens downward, congruent with y =x², vertex (-3, 2)(Pvertex (2, - 2), x-intercepts of 0 and 4e)vertex (-1, 4), y-intercept of 2f)vertex (4, 5), passes through (2, 9)Solution4.Describe the transformations applied to the graph of y = x² to obtaina graph of each quadratic relation. Sketch the graph by hand. Startwith the graph of y = x² and use the appropriate transformations.%3Da) y = -4(x – 5)² + 3b) y = 2(x + 1)² – 8(x – 1)² – 5d) y =e) y = - (x – 3)² + 2c)y =(++ 2)² + 1f) y = 2(x + 1)² + 4Solution

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Write an equation of a parabola that satisfies each set of conditions. a) opens upward, congruent with y= 2x, vertex (4, – 1) b) opens downward, congruent with y= vertex (-2, 3) f PPEDS downward, congruent with y= x², vertex (-3, 2)

Write an equation of a parabola that satisfies each set of conditions. a) opens upward, congruent with y= 2x, vertex (4, – 1) b) opens downward, congruent with y= vertex (-2, 3) f PPEDS downward, congruent with y= x², vertex (-3, 2)

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter11: Topics From Analytic Geometry

Section11.1: Parabolas

Problem 33E

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Question

Write an equation of a parabola that satisfies each set of conditions.
a) opens upward, congruent with y = 2x', vertex (4, –1)
b) opens downward, congruent with y =
vertex (-2, 3)
%3D
c) opens downward, congruent with y =x², vertex (-3, 2)
(P
vertex (2, - 2), x-intercepts of 0 and 4
e)
vertex (-1, 4), y-intercept of 2
f)
vertex (4, 5), passes through (2, 9)
Solution
4.
Describe the transformations applied to the graph of y = x² to obtain
a graph of each quadratic relation. Sketch the graph by hand. Start
with the graph of y = x² and use the appropriate transformations.
%3D
a) y = -4(x – 5)² + 3
b) y = 2(x + 1)² – 8
(x – 1)² – 5
d) y =
e) y = - (x – 3)² + 2
c)
y =
(++ 2)² + 1
f) y = 2(x + 1)² + 4
Solution

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