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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