Chapter SH, Problem 9.13EP

To determine

To find: The solution of the equation $x^2=-2x+3$ graphically.

Answer to Problem 9.13EP

The solutions the equation $x^2=-2x+3$ are $-3$ and 1.

Explanation of Solution

Given information:

The given equation is $x^2=-2x+3$ .

Calculation:

The given equation is a quadratic equation.

  $\begin{array}{c}{x}^2=-2x+3\\ x^2+2x-3=0\end{array}$

Write the standard form of the quadratic equation.

  $y=a{x}^2+bx+c$

Compare the given equation with the standard form of the quadratic equation.

  $a=1,b=2,c=-3$

Write the equation for the axis of the symmetry.

  $x=\frac{-b}{2a}$

Substitute $2$ for $b$ and $1$ for $a$ .

  $\begin{array}{c}x=\frac{-\left(2\right)}{2\left(1\right)}\\ =-1\end{array}$

So, the equation for the axis of the symmetry is $x=-1$ .

The vertex is equal to $\left(x,y\right)$ . To calculate the value of $y$ , substitute $-1$ for $x$ in the given equation.

  $\begin{array}{c}y={\left(-1\right)}^2+2\left(-1\right)-3\\ =1-2-3\\ =-4\end{array}$

So, the vertex of the equation is $\left(-1,-4\right)$ .

The y -intercept of the graph of the equation is equal to the value of $c$ . So, the y -intercept of the graph of the equation is $-3$ .

Draw the graph of the equation.

  

From the graph, the graph intersects the x -axis at $-3$ and 1.

Therefore, the solutions the equation $x^2=-2x+3$ are $-3$ and 1.