Which of the following ordered pairs
make the equation y equals
x squared minus five x plus four true?
Check all that apply.
If an ordered pair makes the equation true,
the ordered pair is a solution to the equation.
Every ordered pair consists of two values
where the first value is the x value
and the second value is the y value.
To determine which ordered pairs make the equation true,
we substitute the first value for x
and the second value for y,
and then see if it makes the equation true,
or satisfies the equation.
For the first ordered pair, negative three comma 28,
we substitute negative three for x and 28 for y.
Performing this substitution gives us 28 equals
x squared will be the square of negative three,
and then minus five x will become
minus five times negative three,
and then we have plus four.
Now we simplify the right side.
The square of negative three is positive nine,
so we have positive nine,
and then minus five times negative three
is minus negative 15, which is equivalent to plus 15,
and then we still have plus four.
Nine plus 15 is 24, 24 plus four is 28,
giving us 28 equals 28, which is true,
which means this ordered pair negative three comma 28
makes the equation true, or is a solution to the equation.
For the next ordered pair,
we substitute three for x and negative two for y.
Performing this substitution gives us
negative two equals the square of positive three
minus five times positive three plus four.
Simplifying the right side,
the square of positive three is nine,
and then we have minus 15 plus four.
Nine minus 15 is negative six,
negative 6 plus four is negative two,
negative two equals negative two is true,
and therefore this ordered pair makes the equation true,
or is a solution to the equation.
We also check this ordered pair.
The next ordered pair is zero comma six.
We substitute zero for x and six for y.
Performing this substitution gives us six equals
the square of zero minus five times zero plus four.
Simplifying on the right, zero squared is zero,
minus five times zero gives us minus zero,
and then plus four.
Simplifying, we have six equals four, which is not true,
and therefore this ordered pair
does not make the equation true and is not a solution.
We do not check the box for this ordered pair.
The next ordered pair is one comma zero.
We substitute one for x and zero for y.
Performing the substitution gives us zero equals
the square of positive one minus five times one plus four.
Simplifying, the square of one is one,
minus five times one gives us minus five and then plus four.
One minus five is negative four,
negative four plus four is zero.
This gives us zero equals zero which, again, is true.
This ordered pair makes the equation true and is a solution.
We check the box for this ordered pair.
For the last ordered pair,
we substitute two for x and negative three for y.
Performing this substitution, we have negative three equals
the square of positive two
minus five times positive two plus four.
Simplifying on the right, the square of two is four
minus five times two gives us minus 10, and then plus four.
Four minus 10 is negative six,
negative six plus four is negative two.
Negative three does not equal negative two,
which means this ordered pair does not
make the equation true and is not a solution.
We don't check this box.
Another way to determine
if ordered pairs make an equation true
is to graph the equation
and if the ordered pairs represent points on the graph,
they are solutions, or make the equation true.
If the points are not on the graph they are not solutions,
or don't make the equation true.
So let's also verify this graphically.
The graph of y equals x squared minus five x plus four
is graphed in blue.
Each of the points represented by the ordered pairs
is graphed in red.
And notice how the point given by the ordered pair
negative three comma 28,
the point given by the ordered pair one comma zero,
and the point given by the ordered pair
three comma negative two
are the three points that are on the graph,
and the points given by the ordered pairs
zero comma six and two comma negative three
are not on the graph,
which means they don't make the equation true
and are not solutions.
I hope you found this helpful.