Math Mid-Turn Test

Max or Min Value

The y-coordinate of the vertex is the max/min value

-if the value of a has a negative than it opens down/max value

-if the value of a is a positive than it opens up/min value

How to know vertically stretched/compressed

• |a| > 1 → VERTICAL STRETCH (narrow)

• 0 < |a| < 1 → VERTICAL COMPRESSION (wide)

Examples:

• y = 3(x − 1)² → stretch

• y = ½(x − 1)² → compression

How to know if it goes up or down

Look outside the parentheses.

• + k → shift UP k

• − k → shift DOWN k

shifted to the right/left

Look inside the parentheses with x.

• x − h → shift RIGHT h

• x + h → shift LEFT h

reflected across the xaxis

if graph is a<0

Domain (Word Problems)

1⃣ What does x mean?
(time, distance, money, objects)

2⃣ No negatives
→ x ≥ 0

3⃣ Is there a max?
→ x ≤ max value

4⃣ Objects/people?
→ whole numbers

✏ Examples (tiny)

• Time → x ≥ 0

• Money → 0 ≤ x ≤ total

• Rectangle sides → must be positive

Domain (except for word problems)

All real #s

Range

-Depends on a and k-

If a>0 (opens UP): y≥k

If a<0 (opens DOWN): y≤k

Interval of Increasing

if a has a positive rate of change so you use x_h

Interval of Decreasing

if a has a negitive rate of change so you use x_h

What is Vertex form?

y=a(x-h)² +k

Axis of symmetry (Vertex)

x=h

What is the vertex? (Vertex)

(h,k)

X-intercepts (Vertex)

• Set as y=0

• Isolate the square

• Square root (plus/minus)

• Solve for x

Y-intercepts (Vertex)

Plug in 0 for x and solve for y

Symmetric point (Vertex)

x=2h

What is Standard form?

y=ax²+bx+c

Axis of symmetry(Standard)

x=-b/2a

What is the vertex? (Standard)

You first find the axis of symmetry and then plug into x the equation for y

Y-intercepts (Standard)

(0,c)

Symmetric point (Standard)

(-b/a)

What is Intercept form?

y=a(x-p)(x-q)

Axis of symmetry (Intercept)

x=p+q/2

What is the vertex? (Intercept)

Use the axis of symmetry the you plug the values to find y

X-intercepts (Intercept)

x=p and x=q

Y-intercepts (Intercept)

You plug in 0 for x and then solve for y

Symmetric point (Intercept)

• x-intercepts: 2 and 6

• p+q=8

Opens Down

if a is a negitive

Opens Up

if a is a positive