Chapter 9, Problem 1RVS

Math each equation or inequality with its graph.

$y=-4+4x-x^2$.

To determine

The correct graph from the provided graphs that matches the equation $y=-4+4x-x^2$.

Answer to Problem 1RVS

Solution:

The correct graph from the provided graphs that matches the equation $y=-4+4x-x^2$ is J.

Explanation of Solution

Given Information:

The provided equation is:

$y=-4+4x-x^2$

The provided options are:

Consider the provided equation:

$y=-4+4x-x^2$

For any parabola given by the equation of the form $a{x}^2+bx+c$, the $x$-coordinate of the vertex is $-\frac{b}{2a}$ and the $y$- coordinate of the vertex can be found by substituting $-\frac{b}{2a}$ for $x$ and solving for $y$.

Here in the provided equation:

$y=-4+4x-x^2$

$a=-1$, $b=4$ and $c=-4$

So, the $x$-coordinate of the vertex is $-\frac{4}{2\left(-1\right)}$, that is $2$.

Now, substitute $2$ for $x$ in the provided equation and solve for $y$:

$\begin{array}{c}y=-4+4\left(2\right)-{\left(2\right)}^2\\ =-4+8-4\\ =0\end{array}$

So, from the provided options, the vertex of parabola lying at $\left(2,0\right)$ is the option J.

Therefore, the correct graph from the provided graphs that matches the equation $y=-4+4x-x^2$ is J.