Nice-Looking Parabolas (3.14.2)

Question 1

• Standard form of a parabola: f (x) = ax^2 + bx + c.

Answer 1

• Standard form of a parabola: f (x) = ax^2 + bx + c.

Question 2

• Vertex of a parabola: (h, k).
• h = –b/2a.
• k = f (h).

Answer 2

• Vertex of a parabola: (h, k).
• h = –b/2a.
• k = f (h).

Question 3

• Standard form for parabola showing vertex: f (x) = a (x - h)^2 + k.

Answer 3

• Standard form for parabola showing vertex: f (x) = a (x - h)^2 + k.

Question 4

The direction a parabola opens is easy to determine. Look
at the coefficient of the squared term in the function.
If the coefficient is positive, the curve opens in the positive
direction.
If the coefficient is negative, the curve opens in the negative
direction.

Answer 4

The direction a parabola opens is easy to determine. Look
at the coefficient of the squared term in the function.
If the coefficient is positive, the curve opens in the positive
direction.
If the coefficient is negative, the curve opens in the negative
direction.

Question 5

First, consider the standard form of a parabola:
f (x) = a (x – h)
2
+ k
Then look at this example. The vertex (h, k) is easily
determined to be (–3, –4).
Remember: h is subtracting so change the sign of the
x-value before using it in the vertex.

Answer 5

First, consider the standard form of a parabola:
f (x) = a (x – h)
2
+ k
Then look at this example. The vertex (h, k) is easily
determined to be (–3, –4).
Remember: h is subtracting so change the sign of the
x-value before using it in the vertex.

Question 6

Notice: Downturning parabolas have negative coefficients
on the squared term in their equations.
Notice: The x-value changes sign as a coordinate from what
is used in the equation.

Answer 6

Notice: Downturning parabolas have negative coefficients
on the squared term in their equations.
Notice: The x-value changes sign as a coordinate from what
is used in the equation.