By Hudson Brock
A parabola is a curve where any point is at an equal distance from
- a fixed point (the focus), and
- a fixed straight line (the directrix)
- Solve (x + 1)(x – 3) = 0.
Example is in picture
Axis of symmetry
Ex, This is a graph of the parabola y = x2 – 4x + 2 together with its axis of symmetry x = 2.
The axis of symmetry is the red vertical line.
Ex, The quadratic function f(x) = 9 - x2 has the maximum value of 9.
Ex, The quadratic function f(x) = 16 + x2 has the minimum value of 16.
A Term is either a single number or a variable, or numbers and variables multiplied together.
Ex, An Expression is a group of terms (the terms are separated by + or - signs)
So, now we can say things like "that expression has only two terms", or "the second term is a constant", or even "are you sure the coefficient is really 4?"
To find the first differences, subtract successive y-values for equal steps of x-values
These are tables
1, 1, 2
2, 3, 2
3, 5, 2
- Difference means the answer of a subtraction equation, such as 4-2=2 the second difference is the second answer to a multi part equation.
Example in picture
Ex, Show that if (2+i) is a zero to f(x)=-x2+4x-5 then 2-i is also a zero of the function