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

2 Answers
Apr 3, 2018

Answer:

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 #y=x^2 - 14x^2 + 24# is
#x^2 - 14x^2 + 24=0#. This makes it easier as it is now a written as a simple quadratic, ready to solve.

So, firstly, the product and sum of #y=x^2 - 14x^2 + 24# is:
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

Apr 3, 2018

Answer:

Algebraically first then plot the graph

Explanation:

#y= x^2 -14x +24# factorises to #y =(x-12)(x -2)#
So the #x# intercepts are when #y= 0#
This is when #x= 12 #. or #x= 2#

The #y# intercept is 24 (when #x# =0)
To find the turning point, use completing the square:

#y = x^2-14x+24#

#=># # y=(x-7)^2-25# so the turning point is (7,-25)

To do it graphically, it is a #u# shaped parabola that comes down through (0,24) then through (2,0) through the minimum (7,-25) and back up through (12,0)