Download Example 1

1st step: Find the GCF if possible
2nd step: Multiply a and c
3rd step: Then find two numbers that add up
to b and multiply to the product a times c
gave you.
4th step: You need to put both numbers over
a.
5th step: Reduce as much as possible.
3x²-15x+12=0
X²-5x+4=0
4
-5
-4,-1
1 1
X= 4, 1
m²+11m+30=0
30 11
5,6
1 1
X= -5, -6
3x²-9x+24=0
x²-3x+8=0
8
-3
-4 , -2
1 1
X= 4, 2
The Equation used for Quadratic Function is x=
ax²+bx+c. They Graph parabolas.
The Difference between a quadratic function and a
linear function is that the graph of a quadratic
function is a parabola, whereas the graph of a linear
function is just a straight line, also you use the slope
intercept form of a line in linear function which is
y=mx+b and in Quadratic functions we use x=
ax²+bx+c.
1. Is this equation used for a Quadratic function or a
linear function? 3x²+5x+11 ( A quadratic ,remember
the a is squared.
2. Is y=mx+b formula used for linear or quadratic
functions?
3. When you are given a graph with an image like this
you know that it is a linear function. But
When you are given an image like
you know it is a quadratic function.
The Quadratic Graphing Formula is a(x+b)²+c=0.
A: changes steepness depending if the parabola is going
up or down, if a is less than 0 the parabola will be going
down and if a is greater than 0 the parabola will be
going up. Also if a is greater it is more steeper and if a is
less that 0 the the parabola is less steeper.
B: moves right or left, b units moves opposite if positive
it goes left and if negative it goes right.
C: moves vertex up or down , C unit if it is positive it
goes up and if it is negative it goes down.
y=x^2
y=x^2-2x+8
y=-.5x^2+2x
1st step: Set the equation equal to zero
2nd step: Make a T-table
3rd step: Find the vertex x=b/2a
4th step: Then put your vertex solution on the x
side of the table and add two more numbers
5th step: Solve them, then graph your Parabola
Find the x-values where it crosses the x-axis
A solution is a method or process of solving a
problem which is a true statement
Y=-x2 X=0
X=0
No SOLUTION
1st step: Be sure that x² is by itself.
2nd step: Then make sure there is no longer x
3rd step: Square root both sides
4th step: reduce as most as possible
5th step: don’t forget your +or-
a²-16 = 0
+16 +16
a² = 16
a= + or -4
m²+9=0
-9 -9
m²= -9
m= + or - 3
3x²-75=0
+75 +75
3x²= 75
3
3
x² = 25
x= +or - 5
1st Step: Find your A, B, and C.
2nd Step: Multiply a times c
3rd Step: Then on the T-table on one side put the solution
of a x c and on the other put b
4th Step: Then find 2 numbers that when being added
sum to b and when being multiplied to the solution a
times c gave you.
5th Step: Reduce as much as possible.
1st Step: Get x² =1
2nd Step: Then you need to get C by itself
3rd Step: Complete the square ( First get a =1, then find
b, divide b/2, square it b/2² and finally factor (x+b/2)² )
4th Step: Add (b/2)² to both sides
5th Step:Finally square root both sides and DON’T
FORGET + or -
a²+2a-3=0
+3 +3
a²+2a=3
(a+1)²= 3+1
a+1= +or-2
A= 3, 1
x²+8x=9
+16 +16
(x+4)² = 25
x+4 = + or -5
-4
-4
X= 1, -9
m² -12m+26=0
-26 -26
m²- 12m = -26
+36 +36
m²- 12m =10
(m+6)² = 10
m-6= +or- 10
+6
+6
M= 6, +or- 10
The Quadratic Formula is x= -b +or-√b² - 4ac
2a
1st Step: Find your A, B, and C.
2nd Step: Fill in the formula with your
numbers
3rd Step: SOLVE!
THE DISCRIMINANT IS :
X² -5X -6 =0
x= 5 +or- 25-4 (-6)
2
x= 5 +or- 4
2
X= 5 +or- 7
2
3w²+5w-7=0
x= -5 +or- 5²-4 (3)(-7)
2(3)
x= -5 +or- 25+84
6
x= -5 +or- 109
6