SOLUTION: Sketch the graph of y =

SOLUTION: Sketch the graph of y = | x^2 - 5x + 4 |

Question 1184512: Sketch the graph of y = | x^2 - 5x + 4 |
Found 2 solutions by Theo, ikleyn:
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
three graphs.

first is y = x^2 - 5x + 4

second is y = |x^2 - 5x + 4|

third is both.

red is the first and blue is the second.
they are the same except for the piece that is negative (red piece).

that's where the first is negative and the second is positive, because that's the absolute value part.

absolute equation property.

is x is positive then |x| is equal to x.
if x is negative, then |x| is equal to -x.

the value of |x| is always positive.

here's a reference on absolute value.

https://www.mathsisfun.com/numbers/absolute-value.html

Answer by ikleyn(52781) (Show Source): You can put this solution on YOUR website!
.

First, you sketch the normal/usual parabola x^2 - 5x + 4.

Then you find the part of this parabola, which is located in the lower half of the coordinate plane below x-axis.

This part is between the roots of the given quadratic function, whose roots are 4 and 1.

Next, you reflect this part of the parabola about x-axis, considering x-axis as a mirror.

Another way is to use automatic/electronic plotting tool/tools from the Internet.

For example, from this link
www.desmos.com
or from other similar sites.

Then the only need is to write the formula of the function in the assigned window, and the tool will make all the rest work for you,
plotting a graph is seconds. A benefit is that you do not need to think.

Third way is to use your graphing calculator.

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