Quadratic Functions
How do you graph a quadratic function?
You first set you equation to 0 so for example: 5x^2-20x+15=0. Now since each term is divisible by 5, you can divide by 5. So now the equation you have is x^2-4x+3=0. Now you put it in factor form which is (x-3)(x-1). Then you factor that. And once you factor it, you get your x values. So x=3 and x=1. And then you plug it in the graph and you get your answers.
Whats a linear function?
A linear function represents a straight line on a graph
What's the formula for graphing a function?
y=f(x)
What's the equation for an exponential function?
y=I(r)^x
How do you find the vertex of a quadratic function?
You use the equation x=-b/2(a)
Whats the equation for a linear function?
y=mx+b
Plug in your values for x and solve. Should end up with a line with a positive slope.
Whats an exponential function?
When you are multiplying or dividing... it is exponential.
How do you find the line of symmetry?
You first need to find the vertex. Then once you find the vertex say (-1,-1) for example, -1 will be your line of symmetry.
How do you know if a function is linear?
A function is linear if you add or subtract
What do you do to graph functions?
You plug in any value for x and solve with the remaining equation. You should use numbers for -2 through 2.
What does the exponential equation stand for/what does it mean?
I=initial value or the y-intercept
r=the value being multiplied or divided every time
What is a quadratic function?
one of the form f(x) = ax^2 + bx + c, where a, b, and c are numbers with a not equal to zero
What's does the y=mx+b equation mean/stand for?
y=dependent variable
m=slope
x=independent variable
b=the y-intercept or starting value
Why do we make tables to help us graph a function?
To give is the possible points to make a line.
If x is 0, then your I(y-intercept) would be?
Whatever is next to the 0 on the table graph. So in this example it is 3:
x,y
0,3
1,19
2,36
3,52
and so on.
How to find the zeros?
You first have to put your equation in factor form so example 3x^2+7x+2=0 so (3x+6) (3x+1) and that is in factor form. You then solve that. And once you do, you will get your zeros.
Solve this linear equation: 5x - 11 = 3x + 9
Answer=10
Solve: f(x)=−2x+1
f(x)=7
Solve:
x, y
-1, 0.4
0, 2
1, 10
2, 50
y=2(5)^x