Quadratic Functions

Question 1

What is the base case of Quadratic Functions?

Answer 1

y = x^2

Question 2

What is the complete form of the Quadratic Function?

Answer 2

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

Question 3

Which value can affect the thin and wildness of the parabola?

Answer 3

a

a < -1 or a >1 k
parabola thinner than y=x^2

-1 < a < 1, a ≠ 0
Parabola wider than
y =x^2

Question 4

Which value affects which side the parabola opens to?

Answer 4

a

If a >0, parabola open upwards.

If a <0, parabola open downwards.

Question 5

Describe shift of the parabola from the base case.
y = x^2 + 5

Answer 5

Shift up by 5 units.

+ k shifts parabola upwards.
- k shifts parabola downards

Question 6

Describe shift of parabola from the base case.
y = (x+10)^2

Answer 6

left shift by 10 units

+ h shifts the parabola leftwards.
- h shifts the parabola rightwards.

Question 7

Describe shift of parabola from the base case.
y = -0.5x^2

Answer 7

• Open dowwards due to a being being negative.
• Horizontally streched (wider due to a being in between 0 and 1.

Question 8

y = -4(x+10)^2-5

Answer 8

• Open downwards due to a being negative.
• Vertically streched. (thinner due to a being greater than 1.
• Left shift by 10 units.
• Down shift by 5 units.

Question 9

How to find line/axis of symmetry?

Answer 9

-b / 2a
Axis of symmetry is x = _

Question 10

How to find vertex?

Answer 10

Plug in axis of symmetry x = _ into equation.
Solve to find y.

Question 11

How to find the x and y intercepts?

Answer 11

Y intercept: plug in x=0
X intercept: plug in y=0.