Question
Asked Dec 16, 2019
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10. For the functions f(x) = x² + 4x – 14 and h(x) = -(x +5)² +2 find the
following:
(A) Intercepts and the domain, (B) Vertex, (C) Maximum or minimum,
(D) Range, and (E) Write a brief verbal description of the relationship
between the graph of the above quadratic and the graph of g(x) = x².
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10. For the functions f(x) = x² + 4x – 14 and h(x) = -(x +5)² +2 find the following: (A) Intercepts and the domain, (B) Vertex, (C) Maximum or minimum, (D) Range, and (E) Write a brief verbal description of the relationship between the graph of the above quadratic and the graph of g(x) = x².

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Expert Answer

Step 1

Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for you. To get remaining sub-part solved please repost the complete question and mention the sub-parts to be solved.

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Given: f (x)=x²+4x-14 h(x)=-(x+5) +2

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Step 2

Part (A):

Find Intercept:

Consider f(x)=y.

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Intercepts for f(x)=x²+4x-14: To find y- intercept: Put x =0. f (x)=0² +4(0)–14=-14 y- intercepts: (0,-14). To find x- intercept: Put y =0. 0 =x² +4x-14 Use Quadratic equation. 42 -4·1(-14) -4+, 2.1 x=-2+3/2 x- intercepts: (-2+3/2,0),(-2-3/2,0).

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Step 3

Consider h(x)=y.

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Intercepts for h(x)=-(x+5)-+2: To find y- intercept: Put x =0. h(x)=-(0+5)´+2=-25+2=-23 %3D y- intercepts: (0,-23). To find x- intercept: Put y =0. 0=-(x+s}?+2 = (x+5}? =2 =(x+5)=+V2 =x=tV2-5 x- intercepts: (V2-5,0).(-/2-5,0)

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