M6: Graphing Quadratic Functions

Question 1

What is a quadratic function?

Answer 1

f(x) = ax^2+bx+c where a,b,c are not equal to 0

Question 2

What is a parabola?

Answer 2

The graph of a quadratic function that shapes to be a curve.

Question 3

What is the vertex?

Answer 3

The point at which the graph starts at.

Question 4

What is the axis of symmetry

Answer 4

It is a dashed line that goes through the middle of the graph.

Question 5

What is the domain?:

Answer 5

Domain is all the x values on the graph.

Question 6

What is the range?:

Answer 6

Range is all the y values on the graph.

Question 7

What is the maximum value of a parabola?

Answer 7

The biggest y value on the graph.

Question 8

What is the minimum value of a parabola?

Answer 8

The smallest y value on the graph.

Question 9

find the domain and range:

g (x) = −3 x ^2

Answer 9

Domain: (−∞,∞)
Range:[0,-∞)

Question 10

What variable in a quadratic function has to change how wide the graph goes?

Answer 10

a

Question 11

Graph and find the domain and range:

g(x) = -4x^2 - 12x - 8

Answer 11

Points: (-4, -24) (-3, -8) (-3/2, 1) (-1, 0) (0,-8)
Domain:(−∞,∞)
Range:(−∞,1)

Question 12

What is the vertex form of a quadratic function?

Answer 12

y = a(x - h)^2 + k

Question 13

What are the purposes of the variables h and k?

Answer 13

h and k are used for the horizontal and vertical shift of the graph. They both are also points of the vertex.

Question 14

What are the difference between h and k.

Answer 14

h is the horizontal shift and the x value of the vertex and k is the vertical shift and the y value of the vertex.

Question 15

What would happen if the variable a was negative? If it was positive?

Answer 15

if it was negative the graph would be facing down, and if it was positive it would be facing up.