Graphing Quadratics in All forms

Question 1

What are three forms of quadratics?

Answer 1

Standard Form

Vertex Form

Factored Form

Question 2

What does the standard form of a quadratic look like?

Answer 2

y=ax²+bx+c

Question 3

What does vertex form of quadratic look like?

Answer 3

y=a(x-h)²+k

Question 4

What does factored form of a quadratic look like?

Answer 4

y=a(x-r₁)(x-r₂)

Question 5

What are the three ways to find AOS?

Answer 5

Standard: x= -b / 2a

Vertex: x = h (remember opposite)

Factored: x = (r₁ + r₂) / 2

Question 6

What are three ways to find the VERTEX ?

Answer 6

Standard: vertex @ (AOS, y) plug AOS into equation to finid the y value

Vertex: vertex @ (h,k)

Factored: vertex @ (AOS, y) Plug in AOS to find the y value

Question 7

What are three ways to find the y intercept?

Answer 7

Standard: y int @ c

Vertex: y int @ a*h² + k

factored: y int @ a*r₁*r₂

Question 8

Name the FORM and how to find the AOS, Vertex and Y intercept:

y = ax²+bx+c

Answer 8

Standard form.

AOS @ x = -b / 2a

Vertex @ (AOS, y) find y by pluggin AOS into quadratic

y intercept @ c

Question 9

Name the FORM and how to find the AOS, Vertex and Y intercept:

y= a (x - h)² + k

Answer 9

Vertex Form

AOS @ x = h

Vertex at (h, k) (remember opposite h and just k)

y intercept @ a*h² + k

Question 10

Name the FORM and how to find the AOS, Vertex and Y intercept:

y= a (x-r₁) (x-r₂)

Answer 10

Factored Form

AOS @ x = (r₁+r₂) / 2

Vertex at (AOS, y) find y by pluggin AOS into equation

Y intercept @ a*r₁*r₂

Question 11

Why is it called “vertex form”?

Answer 11

Because it shows the vertex explicitly. The vertex is right there in your face.. at (h,k)

Question 12

Why is it called “factored form?”

Answer 12

Because the quadratic is factored completely.

Question 13

What is the bonus you get when an equation is in factored form?

Answer 13

You get the roots (remember opposites)

Roots are also known as:

x-intercepts, zeros, solutions,

Question 14

What are other names for the roots of a quadratic?

Answer 14

ZEROS or SOLUTIONS or X- INTERCEPTS

Question 15

What are the names of the terms in a quadratic in standardform?+y = ax²+bx+c

Answer 15

ax² is quadratic term

bx is linear term

c is constant term

Question 16

What are the three forms of a linear equations?

Answer 16

Standard

Point Slope

Slope Intercept

Question 17

How are linear equations different from quadratic equations?

Answer 17

Linear equations only have an x and their graph is a line.

quadratics have an x² and their graph is a parabola