# How do you solve the equation #x^2-2x-24=0# by graphing?

##### 2 Answers

#### Explanation:

Given:

#x^2-2x-24=0#

I notice that the question asks to graph to solve. I would usually do the reverse: solve to graph, but let's have a look...

Let:

#f(x) = x^2-2x-24#

Evaluating for a few values we find:

#f(0) = color(blue)(0)^2-2(color(blue)(0))-24 = 0-0-24 = -24#

#f(1) = color(blue)(1)^2-2(color(blue)(1))-24 = 1-2-24 = -25#

#f(2) = color(blue)(2)^2-2(color(blue)(2))-24 = 4-4-24 = -24#

Interesting!

Notice that

Since this is a quadratic in

At this point we could note that the multiplier of the

We can check our deduction:

#f(-4) = (color(blue)(-4))^2-2(color(blue)(-4))-24 = 16+8-24 = 0#

#f(6) = color(blue)(6)^2-2(color(blue)(6))-24 = 36-12-24 = 0#

Here's the actual graph, with some of the features we have deduced:

graph{(y-(x^2-2x-24))(x-1+0.0001y)(10(x-1)^2+(y+25)^2-0.1)(10x^2+(y+24)^2-0.1)(10(x-2)^2+(y+24)^2-0.1)(10(x+4)^2+y^2-0.1)(10(x-6)^2+y^2-0.1) = 0 [-10, 10, -30, 15]}

An algebraic solution is not asked for.

Draw the graph and read the values of the

#### Explanation:

The first step is to draw the graph of

You can do this by choosing several

Plot the points and draw the parabola.

You could also find the significant points by calculation:

The

The axis of symmetry and hence the turning point.

The

Once you have the graph, you can turn your attention to answering the question:

solve

If you compare the equations:

you will realise that

The question being asked is "Where does the parabola cross the

You can read these values as the

These are seen to be

graph{y= x^2 -2x -24 [-10, 10, -5, 5]}