Learning About Quadratics
Fun With Quadratics!
In quadratics 1, I learned about owrabola's, how to read them and how to plot them. Finding all the points to the parabola (vertex, axis of symmetry, x and y intercepts) took a lot of steps but once I got the hang of it, it got easier. The most easiest thing I learned was what it meant when a parabola opened upwards compared to downwards.
Quadratics 2 was slightly easier now that I sort of got the hang of quadratics 1. I learned about quadratics relations and equations like vertex form, standard form and factored form.
Finally, in quadratics 3 I was taught how to solve quadratic equations in all 3 different forms.
Quadratics is a tough unit to fully learn but once I got the hang of each chapter, I understood it more than before.
What is quadratics?
Standard form: y=ax2+bx+c
Factored form: y=a(x-r)(x-s)
What is a Parabola?
a < 0 opens down
a > 0 opens up
a and b will give you the axis of symmetry, also known as the line that is parallel to the parabola.
To find the axis of symmetry use this equation:
x= - b/2a
X intercepts are also called "zero's".
Optimal value simply means the lowest of highest point in a parabola, for example, where ever the U shape touches (whether we're looking for the lowest or highest point) that would be the optimal value.
Completing the square:
You take the square root of not one, but BOTH sides...
X- 4 = +/- square root(5)
X=4 +/- square root(5)
X=4- square root (5) and x= 4 + square root (5)
Example from: purplemath.com
- the h value of vertex
-divides the parabola in half
-the k value of vertex equation
Ex: y= -(x+7)3+4
Optimal value= 4
To find axis of symmetry:
Add the 2 x intercepts together and divide by 2
= x value for your vertex
To find y value:
Sub in x and solve for y in the original equation order.
-difference of square
Write an expression using numbers that can multiply to make that expression
Ex: 3x+6 is 3 (x+2)
Make coefficient for "a" = 1.
You should choose two numbers that can multiply to the c value and add up to the b value.
To factor complex trinomials, you should use the method "Guess and Check".
Ex: 3x2 + 13x + 12 factores into ( x + 3) (3x + 4)
=3x2 + 4x + 9 x + 12
=3x2 + 13x + 12
DIFFERANCE OF SQUARES:
what is it?
When the middle term cancels out and has same values but different signs.
Ex: x4 - 7 is x4 + x0 - 7
REMEMBER: a trinomial is a difference of square if it looks like a2 - b2 = (a +b) (a -b)