Exploring Quadratic Functions and Parabolas, Exercises of Mathematics

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• MODULE

1. Define a parabola;
2. Determine the standard form of the equation of a parabola; and
3. Graph a parabola given an equation in vertex form

If 𝑦= ax

2

+ bx + c can be written in the

vertex form 𝑦 = 𝑎 𝑥 − ℎ

2

+ 𝑘 , then

𝑏 𝑎

and 𝑘 =

4 𝑎𝑐 − 𝑏 2 4 𝑎

The point (ℎ, 𝑘) the parabola which is the

graph of 𝑦 = 𝑎 𝑥 − ℎ

2

+ 𝑘 is the vertex,

𝑏 𝑎

and 𝑘 =

4 𝑎𝑐 − 𝑏 2 4 𝑎

Directions: Determine the highest and lowest value of each function by identifying the y-coordinate of the vertex.

1. 𝑦 = 𝑥 2

• 3 𝑥 − 6

2. 𝑦 = −𝑥 2 − 5 𝑥 + 7
3. 𝑦 = − 3 𝑥 − 5 2

• 2

4. 𝑦 = 𝑥 + 1 2 − 3
5. 𝑦 = − 𝑥 − 7 2 − 11
6. 𝑦 = 6 𝑥 2

• 𝑥 − 35

➢ The fixed point is called the focus , while the fixed line is the directrix. ➢ The axis of symmetry divides the parabola into two parts. ➢ The vertex of the parabola is a point that lies on the axis of symmetry. ➢ The distance from the vertex to the focus (or directrix) is called the focal distance (a). ➢ The latus rectum is a segment containing the focus, with endpoints on the parabola and perpendicular to the axis of symmetry.