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In order to determine the y-intercept, sub in 0 for x and then solve the equation.

How to determine the y-intercept?
How to determine the x-intercepts?
EXAMPLE:

y = -4(x-10)^2 + 144

 y-intercept: Set x=0

 

                   y = -4(x-10)^2 + 144

                y = -4(0-10)^2 + 144

                y = -4(-10)^2 + 144

                y = -4(100) + 144

                y = -400 + 144

                y = -256

Therefore the y-intercept in (0,-256).

In order to determine the x-intercepts, sub in 0 for y and then solve the equation.

Therefore, the x-intercepts are (4,0) and (16,0).

Before this step, we have been solving this equation just as we would normally solve an equation. However, at this step, we must square root the equation, but referring back to the rules of square roots, there are 2 possible square roots: a positive and a negative. So we branch out our solution into 2 to find our 2 solutions.

Solving Quadratic Equations

To solve quadratic equations means to find the x-intercepts or zeros of the parabola. In order to find the zeros of a parabola, set 'y' to 0 and then simply solve the equation. To find the y-intercept of the parabola, set 'x' to 0 and then solve the equation! However, before solving quadratic equations, it is crucial to understand square roots.

Square Roots

To square a number means to multiply it by itself.

 

               EXAMPLE:

                                                       5^2 = 25

 

On the other hand, square roots work the other way around. To square root a number means to find a value that can be multiplied by itself to give the original number.

               

               EXAMPLE:

                                                         âˆš25 = 5

 

This seems simple, however, there are some rules to square root a number. The first rule is that you cannot square root a negative number as the only way for two numbers to give a product of a negative number is if the factors are opposite integers. However, to square root a number is to get an integer that will give a product of the original number when multiplied by itself.

 

             EXAMPLE:        

                                                       -25 = (-5) x (5)

                                                       

                                                     âˆš(-25) = ERROR

                                      

                                                         âˆš25 = 5

 

But, a negative number can be squared! This is because a negative times a negative will give a positive number and it is possible to have square roots of positive numbers.  This is why when you square root a number, there are two possible values, a negative square root or a positive square root.

 

            EXAMPLE:              

                                                     (-5) x (-5) = 25

                                                        (5) x (5) = 25

                                                                25 = 5 or -5

How do square roots relate to solving quadratic equation?
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