Question
The function \( h \) is defined as follows. \[ h(x)=-2 x^{2}+1 \] If the graph of \( h \) is translated vertically upward by 7 units, it becomes the graph of a functio Find the expression for \( g(x) \). Note that the ALEKS graphing.calculator may be helpful in checking your answer. \( g(x)=\square \)
Ask by Clark Mullins. in the United States
Feb 22,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( g(x) = -2x² + 8 \)
Solution
The original function is h(x) = -2x² + 1. After shifting the graph up 7 units, you add 7 to the function value for each x. This gives:
g(x) = h(x) + 7
g(x) = (-2x² + 1) + 7
g(x) = -2x² + 8
Thus, the expression for g(x) is g(x) = -2x² + 8.
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Simplify this solution The Deep Dive
To translate the graph of the function \( h(x) = -2x^2 + 1 \) vertically upward by 7 units, you simply add 7 to the entire function. So, the expression for \( g(x) \) becomes: \[ g(x) = h(x) + 7 = -2x^2 + 1 + 7 \] Now, combine like terms: \[ g(x) = -2x^2 + 8 \] Thus, the expression for \( g(x) \) is: \[ g(x) = -2x^2 + 8 \]
