# How do you solve #y = x^2 − 14x + 24# graphically and algebraically?

##### 2 Answers

There are 3 ways to solve this quadratic algebraically. The most simple way to solve your problem would be to use the product and sum method.

#### Explanation:

Before we begin, another way to write

So, firstly, the product and sum of

Product =24

Sum = -14

Now the next step is to find two numbers that will give you a product of 24 and a sum of -14.

P: -12*-2 =24

S: -12 + (-2) =14

Therefore your product and sum are -12 and -2.

Next, write these numbers in an expanded quadratic form:

(x-12)(x-2)=0

Now simply solve using null factor law:

12-12=0

2-2=0

Therefore x=12 or 2

Algebraically first then plot the graph

#### Explanation:

So the

This is when

The

To find the turning point, use completing the square:

To do it graphically, it is a