Q12. - Algebra 1

Question

Solve each equation by graphing. If integral roots cannot be found, estimate the roots to the nearest tenth.

 $x^2=12$

Step-by-Step Solution

Answer

The roots of the equation $x^2=12$ are $\mathit{x}\mathbf{=}\mathbf{-}\mathbf{3}\mathbf{.5}$ and $\mathit{x}\mathbf{=}\mathbf{3}\mathbf{.5}$.

 

Step 1. Define the standard form of the quadratic function.

A quadratic function, which is written in the form, $f\left(x\right)=a{x}^2+bx+c$, where, $a\ne 0$ is called the standard form of the quadratic function.

Step 2. Rewrite the equation x 2 = 12 in the form f x = a x 2 + b x + c .

Write the equation $x^2=12$ in standard form.

The standard form of this equation is

 $x^2-12=0$

Write the equation $x^2-12=0$ in the form $f\left(x\right)=a{x}^2+bx+c$.

 $f\left(x\right)=x^2-12$

Step 3. Plot the graph of the function f x = x 2 − 12 .

The graph of the function $f\left(x\right)=x^2-12$ is shown below.

Step 4. Solve the equation x 2 = 12 from the graph of the function f x = x 2 − 12 .

Observe the graph of the function $f\left(x\right)=x^2-12$.

The graph intersects the  $x$- axis at the points near about $x=-3.5$ and  $x=3.5$.  

Therefore the roots of the equation $x^2-12=0$ are $x=-3.5$ and $x=3.5$ .