Chapter+10

Quadratic Functions (2x^2+3x+6=0) 10.1 graphing f(x) ax^2+bx+c change f(x) to y Rules 1. highest degree of the quadratic is always 2. 2. All exponets must be positive When graphing a quadratic: 1. Create a table 2. Plot Points 3. Connect the dots!

Axis of Symmetry- formula x=-b/2a Examples y=x^2-4 1. Find axis or symmetry x=-0/2(1) x=0 x:-2,-1,0,1,2 y: 0, -3,-4,-3,0 graph y=x^2-3x+2 X=3/2=1.5 Take 3/2 and put it back into the original equation 1.write equation 2. find axis of symmetry 3. take axis and solve y value 4. plot the point 5. Determine Direction 6. Create a table w? at least 2 values 7. Plot points

My Steps 1.Write equation in x=b/2a form 2.Do the equation to find the x value of the vertex 3.Plug that value back in to find the y value of the vertex 4.Graph this point 5.Make a table putting your vertex in the middle 6.Graph these points &. Connect your lines 10.2 Solve quadratic equasions by graphing Estimate solutions of quadratic equasions by graphing.

x^2-3x-10=0 the solutions set is the roots their will be 2 so thier will be 2 x intercepts

when you have 1 root it becomes: vertex axis of symmetry x-intercept Integral Roots- popsitive or negative numbers in solution set My Steps 1. See if their are two numbers that add to equal,but multiply to equal C 2.If this doesn't work you solution is null. 3. If this does work these two numbers are you vertex 4. Put these numbers in the middle of the table 5. Graph 10.3 Solve Quadratics by completing the square Here are the steps (perfect square trinomials) 1. Write the original equation 2. Factor 3. Take the square root of each side 4. Solve for the variable (remember you will have a positive and a negative solution to the square root) 5. Write your solution set.

Here are the steps (NON - perfect square trinomials) 1. Write the original equation a. You realize that you can not factor so you subtract the constant (number) from both sides to get ax^2 + bx b. simplify c. Find a number that you can add to both sides by using the equation (b/2)^2 d. Add this number to each side e. simplify 2. Factor 3. Take the square root of each side 4. Solve for the variable (remember you will have a positive and a negative solution to the square root) 5. Write your solution set. ft/speed distance
 * find each value that makes x a perfect square*

10.4 Quadratic Formula __x=-b+-Square root b^2- 4a__ 2a All values must be on 1 side of the equation. 1.) g^2+2g-3=0put it into the equation use order of operations Slip the problem in two find solution set if discriminate is... less than zero their is no solution set or roots. =0 their is one root greater than zero two numbers 10.5 Graphing exponental Functions y=7^x If the exponent is negative you need to change the problem to a fraction. division or multiplication problem has exponental behavoir subtraction and addition No exponental behavoir

10.6 Growth- y=c(1+r)^t y=final amount c= inital amount r= rate of change (decimal) t=time

Decay (decreasing)- y=c(1-r)^t y=final amount c= inital amount r= rate of change (decimal)

Compound Interest-A=P(1+r/n)^n/t A= Balance P= Inital amount r= annual rate n= number of times compound per year t= time(years)

10.7 Geometric sequences Finding the pattern 2,6,18,54 multiply by 3 a=a*1*r^(n-1) A= first term r common ratio (number your multiplying by) n term number

__Vocabulary__ 10.1 Quadratic- function- Parabola- U shaped line opening down or up. If it opens up A value is positive, and vertex is a minimum value. If opens down a value is negative, and vertex is a maximum value. Minimum- small Maximum- big Vertex- where it peaks high or low Symmetry- the same;equal Axis of symmetry- 10.2 Quadratic equation- Roots- solutions to the quadratic equations Zero- x intercepts 10.3 Completing the square- Vertex form- 10.4 Quadratic formula- Discriminant- Square root b^2- 4a

10.5 Exponential function- 10.6 Exponential growth- Exponential decay- Compound interest- 10.7 Geometric sequence- Multiplying and dividing Common ratio- Geometric means-

Extra Notes 10.1