# How do you solve #y = x^2 -8x + 16# graphically and algebraically?

##### 2 Answers

see below

#### Explanation:

Graphically

the roots are where the graph crosses the

that is when

graph{x^2-8x+16 [-3.74, 14.04, -2.56, 6.33]}

As can be seen from the graph it touches the

Algebraically

we could use factorising., completing the square or the formula.

look for factorising first

the repeated brackets show that we have repeated roots, and that the

Let's solve it algebraically first:

We solve this by finding the "zeros" or x-intercepts of the equation. To do this, we factor the equation, if possible.

We need to find 2 numbers (can be the same) that add up to

So our equation is:

Since we are finding the x-intercept(s), let's set

To simplify this, let's root both sides by

So the x-intercept is at

To graph this, we find the vertex and the slope.

In this case, since there is only one x-intercept, that means that it is the vertex.

The slope depends on the coefficient, or the number in front of the highest degree term.

Let's graph this now!

As you can see, the x-intercept is the same as the vertex.

Hope this helps!