Question

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

Answer 1

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 and 0` and is much closer to `-1` than `0`, and

• the other is between `-5 and -6` and much closer to `-5` than `-6`

Answer 2

`x=-1.75 and x= -5.25`

Explanation:

First you need to have a graph of the parabola `y = x^2+6x+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:

`color(red)(y) = x^2+6x+4`
`color(red)(0)= x^2+6x+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 and x= -5.25`

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