Chapter SH, Problem 9.12EP

To determine

To find: The solution of the equation $-2x^2-2x+4=0$ graphically.

Answer to Problem 9.12EP

The solutions the equation $-2x^2-2x+4=0$ are $-2$ and 1.

Explanation of Solution

Given information:

The given equation is $-2x^2-2x+4=0$ .

Calculation:

The given equation is a quadratic equation. 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.

  $a=-2,b=-2,c=4$

Write the equation for the axis of the symmetry.

  $x=\frac{-b}{2a}$

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

  $\begin{array}{c}x=\frac{-\left(-2\right)}{2\left(-2\right)}\\ =-\frac{1}{2}\\ =-0.5\end{array}$

So, the equation for the axis of the symmetry is $x=-0.5$ .

The vertex is equal to $\left(x,y\right)$ . To calculate the value of $y$ , substitute $-0.5$ for $x$ in the given equation.

  $\begin{array}{c}y=-2{\left(-\frac{1}{2}\right)}^2-2\times \left(-\frac{1}{2}\right)+4\\ =\frac{-2}{4}+1+4\\ =-0.5+1+4\\ =4.5\end{array}$

So, the vertex of the equation is $\left(-0.5,4.5\right)$ .

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 4.

Draw the graph of the equation.

  

From the graph, the graph intersects the x -axis at $-2$ and 1.

Therefore, the solutions the equation $-2x^2-2x+4=0$ are $-2$ and 1.