top of page
Factored Form
The factored form is y=a(x-r)(x-s)(look back for reference if needed). This equation is often used to solve the zeroes, axis of symmetry, and optimal value as it is very simple to do so with it. We will cover how to solve the x-intercepts, axis of symmetry, and optimal value with this formula.
Zeroes(x-intercepts)
Solving for the x-intercepts is very simple, the variables "r" and "s" represent the x-intercepts. The method used to solve for the x-intercepts is this...
First off we need an example equation, i.e "2(x-3)(x+7)". I will cover this in steps.
Step 1- Look at the r and s values, they are -3 and 7, now do this, write down x-3=0 and x+7=0, this changes according to your values, so...
x-3=0
x+7=0
Step 2- Move the integers over to the right to isolate x, so...
x=3
x=-7
Now you are done finding the x-intercepts, remember the sign changes when you move something over to the other side of the equal sign.
Axis of Symmetry and Optimal Value
Using the same equation as before "y=2(x-3)(x+7)" we will find the axis of symmetry(x) and the optimal value(y). First off we need to solve the x-intercepts, we already have them from before so we will use those, however I will solve them regardless to keep this as simple as possible.
Step 1-
x-3=0
x+7=0
Step 2-
x=3
x=-7
Step 3- Ok we now have our x-intercepts, we will now solve for the axis of symmetry(x) first, you always have to solve for the axis of symmetry first. The first step to doing this is adding the x-intercepts together, so...
x=3+(-7)
x=-4
Step 4- Now you divide your previous answer by 2, in our case -4, so...
x=-4/2
x=-2
Step 5- We now have our axis of symmetry which is -2, now we solve the optimal value(y), to do this simply substitute -2 into x in the equation and solve for y, so...
y=2(-2-3)(-2+7)
y=2(-5)(5)
y=2(-25)
y=-50
We now have solved for the axis of symmetry and optimal value, using these values we can plot the vertex on our graph, it is (-2, -50). Remember that x=axis of symmetry and y=optimal value.
bottom of page