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Expert-verified Found in: Page 156 ### Precalculus Enhanced with Graphing Utilities

Book edition 6th
Author(s) Sullivan
Pages 1200 pages
ISBN 9780321795465 # Determine the quadratic function whose graph is given. The quadratic function whose graph is given is $f\left(x\right)=-\left(x-2{\right)}^{2}+3$ or $f\left(x\right)=-{x}^{2}+4x-1$.

See the step by step solution

## Step 1. Given information.

The given graph is: ## Step 2. Determine the equation.

The vertex is $\left(2,3\right)$, so $h=2$ and $k=3$. Substitute these values into equation $f\left(x\right)=a\left(x-h{\right)}^{2}+k$.

$f\left(x\right)=a\left(x-2{\right)}^{2}+3$

To determine the value of $a$, we use the fact that $f\left(0\right)=-1$ (the y-intercept).

$\begin{array}{rcl}-1& =& a\left(0-2{\right)}^{2}+3\\ -1-3& =& 4a\\ -4& =& 4a\\ -1& =& a\end{array}$

Substitute $a=-1$ in $f\left(x\right)=a\left(x-2{\right)}^{2}+3$.

$f\left(x\right)=-1\left(x-2{\right)}^{2}+3\phantom{\rule{0ex}{0ex}}f\left(x\right)=-\left(x-2{\right)}^{2}+3\phantom{\rule{0ex}{0ex}}f\left(x\right)=-{x}^{2}+4x-4+3\phantom{\rule{0ex}{0ex}}f\left(x\right)=-{x}^{2}+4x-1$

## Step 3. Conclusion.

The quadratic function whose graph is given is $f\left(x\right)=-\left(x-2{\right)}^{2}+3$ or $f\left(x\right)=-{x}^{2}+4x-1$. ### Want to see more solutions like these? 