Quadratic Formula

Quadratic Formula:

Solving quadratic equations from standard form.

If 0 = ax^2 +bc +c

If the standard form equation equals to 0 , to find the x.

Then x= -b + )b^2 -4ac

X-intercepts

When solving using the quadratic formula, there is two things needed. First, you must have your equation in standard form. To start, we will use the equation y= 2x²-2x+124. Next, you must make 'y' equal to 0. So you have 0= 2x²-2x+24. Next, you must know the quadratic formula, which is x= -b+/- √b²-4(a)(c)/2(a). Next, you must know what a, b, and c are equal to.

a=2

b=-2

c=24

Now all you need to do is substitute it into the formula, and solve!

x= -(-2)+/- √2²-4(-2)(24)/2(2)

x+ 2+/- √4+192/4

x= 2+/- √196/4

There are two ways to go from here.

x=198/4

x=49.5

(49.5, 0)

x=2-196/4

x= -194/4

x= -48.5

(-48.5, 0)

Those are your X-Intercepts for your parabola. You still need to find you axis of symmetry though, which is next.

i.e; y= 4x^2 +3x +5

Let y= 0

0= 4x^2 + 3x -5

Note down your values.

a= 4

b= 3

c= 5

Put the numbers in the quadratic formula equation.

x= -3 + )3^2 -4 (4)(-5)

2(4)

x= -3 + )9+80

* You CANNOT find a square root of a negative number.

x= -3 + )89

x= -3+9.4

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*There are two operations going on. One is with positive before the square root and one negative after the square root.

x= 0.8

x=- 1.55

Axis of Symmetry

To find the AOS of an equation in standard form, you will need to first know your 'b' and 'a' values. From the past equation y= 2x²-2x+24, you know your 'b' is -2 and 'a' is 2. So you just substitute those values into the formula given, and you are done.

AOS= (-b/2a)

AOS= -(-2)/2(2)

AOS= 2/4

AOS= 0.5

(x, 0.5)

Optimal Value (sub in)

For this, you just need to sub in the AOS into the 'x' value. So the equation y= 2x²-2x+24 is y= 2(0.5)²-2(0.5)+24.

Then y= 2(0.25)-1+24

y= 0.5-1+24

y= 23.5

Therefore, 23.5 is your y- intercept in this case.