6.1 Graphing
What is quadratic form?
f(x)=ax2 + bx + c
What is zero product property (according to the textbook AND in your own words)?
Textbook: For any real numbers a and b, if ab=0, then either a=0, b=0, or both.
If two things multiply to become zero, then at least one of them must equal zero.
When/why would you use completing the square?
When an equation does not contain a perfect square, you can create a perfect square
Write the quadratic formula
*will write on the board*
What is the general form of a parabola equation?
y=(x-h)^2+k
What is the graph of any quadratic function called? On the graph, what is the axis of symmetry, vertex, and zeros?
The graph of any quadratic function is called a parabola. The axis of symmetry is the vertical line at which the parabola is symmetric. The vertex is where the parabola and axis of symmetry intersect. Zeros are the x-coordinates where the graph intersects with the x-axis.
Factor the following quadratic equation:
0=15x+5x2
0=15x+5x2
0=5x(3+x)
0=5x AND 3+x=0
x=0 AND x=-3
How do you complete the square?
(c/2)2
Solve using the quadratic formula:
x2-10x=24
x=12
x=-2
Name the vertex and axis of symmetry for the graph of f(x)=(x+11)^2+8
Vertex: (-11, 8)
Axis of symmetry: x=-11
Label the quadratic term, linear term, and constant term in the equation f(x)= 4x2 + 3x -5
quadratic term: 4x2
linear term: 3x
constant term: -5
Solve by factoring: x2-5x+4=0
(x-1)(x-4)=0
x-1=0 -> x=1
x-4=0 -> x=4
Find the value of c that makes x2+16x+c a perfect square
x2+16x+c
16/2=8
82=64
Answer: 64
Solve using the quadratic formula:
x2-7x-2=0
*see teacher's edition page 354*
Graph f(x)=4(x+3)^2. Name the vertex, axis of symmetry, and direction of opening for the graph.
graph: *desmos*
vertex: (-3,0)
axis of symmetry: x=-3
direction of opening: up
Solve the following equation by graphing: f(x) = x2-4x+3
*desmos*
Solve by factoring: x2+7x=-10
Rewrite as x2+7x+10=0
(x+2)(x+5)=0
x+2=0 -> x=-2
x+5=0 -> x=-5
Solve by completing the square: x2+6x=16
x2+6x=16
x2+6x+c=16+c
Solve for c: (6/2)2=9
x2+6x+9=16+9
(x+3)2=25
x+3=5; x+3=-5
x=2; x=-8
Solve using the quadratic formula:
x2-3x+7=0
*see teacher's edition page 355*
Write the equation of the parabola that passes through the points at (9,-3) (6,3) and (4,27)
f(x) = 2(x-8)^2 - 5