CPM Homework Help : A2C Problem 4-40

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Home > A2C > Chapter 4 > Lesson 4.1.3 > Problem 4-40

4-40.

Find the vertex of each of the following parabolas by averaging the $x$ -intercepts. Then write each equation in graphing form.

$y=(x−3)(x−11)$
Hint (a):
What are the $x$ -intercepts of this equation? After finding them, average the $x$ -coordinates to find the $x$ -value, and then substitute this value into the equation to find the corresponding $y$ -value.
Answer (a):
$x$ -intercepts: $(3,0)$ and $(11,0)$
vertex: $(7,-16)$
equation: $y=(x-7)^2-16$

$y=(x+2)(x−6)$
Hint (b):
Refer to part (a).
Answer (b):
$x$ -intercepts: $(-2,0)$ and $(6,0)$
vertex: $(2,-16)$
equation: $y=(x-2)^2-16$

$y=x^2−14x+40$
Hint (c):
Refer to part (a).
Answer (c):
$x$ -intercepts: $(10,0)$ and $(4,0)$
vertex: $(7,-9)$
equation: $y=(x-7)^2-9$

$y=(x−2)^2−1$
Hint (d):
First square $(x-2)$ and combine like terms.
More Help (d):
Refer to part (a).

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