Question

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

$x^2+4x-3=0$

Short answer

The roots of the equation $x^2+4x-3=0$ are $\mathit{x}\mathbf{=}\mathbf{-}\mathbf{4}\mathbf{.6}$ and $\mathit{x}\mathbf{=}\mathbf{0}\mathbf{.6}$.

Step-by-step solution

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 x2+4x−3=0 in the form fx=ax2+bx+c. 

Write the equation $x^2+4x-3=0$ in standard form.

This equation is already in standard form.

Write the equation $x^2+4x-3=0$ in the form $f\left(x\right)=a{x}^2+bx+c$.

$f\left(x\right)=x^2+4x-3$

Step 3. Plot the graph of the function fx=x2+4x−3.

The graph of the function$f\left(x\right)=x^2+4x-3$ is shown below.

Step 4. Solve the equation x2+4x−3=0 from the graph of the function fx=x2+4x−3. 

Observe the graph of the function $f\left(x\right)=x^2+4x-3$.

The graph intersects the $x$-axis at the points near about $x=-4.6$and $x=0.6$.

Therefore, the roots of the equation $x^2+4x-3=0$are $x=-4.6$and $x=0.6$.