# How do you use the graph to solve 0=x^2+6x+4?

See below:

#### Explanation:

We're looking for where the graph intersects the X-axis (literally - we're looking for points where $y = 0$, which is the x-axis).

So let's graph the function:

graph{x^2+6x+4 [-10, 10, -5, 5]}

So where does the graph cross the x-axis? Two places:

• one is between $- 1 \mathmr{and} 0$ and is much closer to $- 1$ than $0$, and

• the other is between $- 5 \mathmr{and} - 6$ and much closer to $- 5$ than $- 6$

Oct 1, 2016

$x = - 1.75 \mathmr{and} x = - 5.25$

#### Explanation:

First you need to have a graph of the parabola $y = {x}^{2} + 6 x + 4$

You can do this by working out points and plotting them.

Now compare the equation of the graph with the equation to be solved:

$\textcolor{red}{y} = {x}^{2} + 6 x + 4$
$\textcolor{red}{0} = {x}^{2} + 6 x + 4$

You will see that the two equations are the same, except that where one has $y$, the other has $0$.

This means that we want to know what value of x will give $y = 0$ .
Use the graph to solve this....

$y = 0$ is the equation of the $x -$axis

The question is actually asking, ......
"where does the parabola intersect the $x$-axis?"

Find the values from the graph. $x = - 1.75 \mathmr{and} x = - 5.25$

graph{x^2+6x+4 [-7.655, 2.345, -2.69, 2.31]}