Unit 5: Quadratic Equations and Functions
Trinomial
A polynomial with three terms
Binomial
A polynomial with two terms
root
A solution to a quadratic equation
Linear Term
A term with the variable has a of degree one
Quadratic Term
A term with the variable has a of degree two
quadratic equation
An equation whose greatest exponent is 2
Solving by completing the square
Equation used in order to solve is b/2^2, "b" coming from the bx term
Quadratic Equation
Polynomial with degree 2
What are the zeros of a function?
Same as x- intercepts, roots, solutions to equations
A quadratic equation will have two solutions when...
The graph crosses the x axis in two places
maximum
The highest point of a parabola.
axis of symmetry
The line that cuts the graph into two symmetrical parts; x = -b/2a
minimum
The lowest point of a parabola
vertex
The point (x,y) of a parabola where it crosses the axis of symmetry.
Parabola
The shape of a the graph of a quadratic function
Constant Term
a term that has a number but no variable
domain of a quadratic function
all real numbers
Quadratic formula
allows to calculate the solutions of any quadratic equation.
discriminant
b^2-4ac
Discriminant
b²-4ac
Zero Product Property
if ab=0, then a=0 or b=0
solving by graphing
sometimes when graphing there will be two solutions, either positive or negative. There will also be only one solution which is zero, and there will also be a no solution problem.
Complete the Square
take half of b, then square it. Add to both sides of equation and factor down to vertex form.
A quadratic equation will have no real solutions when...
the parabola does not cross the x axis
y intercept
the point where the graph crosses the y axis
A quadratic equation will have one solution when...
the vertex of the parabola is on the x axis
range of a quadratic function
the y values
Vertex form
vertex= (h, k)
downwards parabola
when "a" is negative
upwards parabola
when "a" is positive
Solve (x + 10)(x + 2) = 0
x = -10, x = -2
Solve (x + 5)(x - 1) = 0
x = -5, x = 1
Solve (x - 10)(x - 2) = 0
x = 2, x = 10
Solve (x - 5)(x + 1) = 0
x = 5, x = -1
Where are zeros of the quadratic equation located on the graph?
x intercepts
Standard form
y intercept: (0, c)
Factor x^2 + 20x + 100
(x + 10)(x + 10)
Factor x^2 + 10x + 25
(x + 5)(x + 5)
Factor x^2 - 20x + 100
(x - 10)(x - 10)
Factor x^2 - 10x + 25
(x - 5)(x - 5)
factored form
(x+3)(x-7)
vertex form
(x-3)^2 - 8 = 0
How many solutions can a quadratic equation have?
0, 1 or 2
To make x^2 + 10x + _____ a perfect square trinomial, add
25
standard form
3x^2 +7x+1 = 0
To make x^2 + 50x + _____ a perfect square trinomial, add
625
To make x^2 -6x + _____ a perfect square trinomial, add
9
Standard Form
This quadratic function is written in ...
Vertex Form
This quadratic function is written in....
solving by square roots
Write the original equation. Isolate x^2 on one side of the equation. Find the square roots of each side and simplify.
