1. Five-Minute Check (over Lesson 9–7) Mathematical Practices Then/Now
New Vocabulary
Example 1: Find the Equation of a Parabola
Example 2: Real-World Example: Write an Equation of a Parabola
Key Concept: Standard Form of Equations of Parabolas
Example 3: Analyze and Graph a Parabola
Lesson Menu

2. Name a radius. A. B. C. D.
5-Minute Check 1

3. Name a chord. A. B. C. D.
5-Minute Check 2

4. Name a diameter. A. B. C. D.
5-Minute Check 3

5. A. 90
B. 120
C. 160
D. 170
5-Minute Check 4

6. Write an equation of the circle with center at (–3, 2) and a diameter of 6.
A. (x + 3) + (y – 2) = 9
B. (x – 3) + (y + 2) = 6
C. (x + 3)2 + (y – 2)2 = 9
D. (x – 3)2 + (y + 2)2 = 6
5-Minute Check 5

7. Which of the following figures is always perpendicular to a radius of a circle at their intersection on the circle?
A. chord
B. diameter
C. secant
D. tangent
5-Minute Check 6

8. Mathematical Practices
1 Make sense of problems and persevere in solving them.
2 Reason abstractly and quantitatively.
4 Model with mathematics.
7 Look for and make use of structure.
Content Standards
G.GPE.2 Derive the equation of a parabola given a focus and directrix. MP

9. You found the equation of a circle by using the Distance Formula.
Derive the equation of a parabola given a focus and directrix.
Then/Now

10. parabola
focus
directrix
axis of symmetry
New Vocabulary

11. Write an equation of each parabola.
Write the Equation of a Parabola
Write an equation of each parabola.
A. focus (0, −4) and directrix y = 4
The vertex is the midpoint between the focus and the directrix.
Use the vertex to find the values of h and k.
(0, 0); h = 0, k = 0
p = 4
The distance between the vertex and the focus is p. The graph points down, so use –p for the equation.
Example 1

12. Write the Equation of a Parabola
Substitute the values into the equation (x – h)2 = 4p(y – k) and simplify.
(x – 0)2 = 4(–4)(y – 0)
x2 = –16y
Answer:
Example 1

13. Write an equation of each parabola.
Write the Equation of a Parabola
Write an equation of each parabola.
B. vertex (–2, 6), focus (–2, –2)
Use the vertex to find the values of h and k.
(–2, 6); h = –2, k = 6
The distance between the vertex and the focus is p. The graph points down, so use –p for the equation.
p = 8
Example 1

14. Write the Equation of a Parabola
Substitute the values into the equation (x – h)2 = 4p(y – k) and simplify.
(x + 2)2 = 4(–8)(y – 6)
(x + 2)2 = –32(y – 6)
Answer: (x + 2)2 = –32(y – 6)
Example 1

15. A parabolic telescope mirror opening upward has
Write an Equation of a Parabola
A parabolic telescope mirror opening upward has
a diameter of 1.5 meters. The distance between
the vertex and the focus is 0.8 meter. Write the
equation of a cross section of the mirror.
Use the vertex to find the values of h and k.
(0, 0); h = 0, k = 0
The distance between the vertex and the focus is p.
p = 0.8
Example 2

16. Write an Equation of a Parabola
Substitute the values into the equation (x – h)2 = 4p(y – k) and simplify.
(x – 0)2 = 4(0.8)(y – 0)
x2 = 3.2y
Answer: x2 = 3.2y
Example 2

17. Key Concept

18. Use the standard form of a parabola to find the vertex (h, k).
Analyze and Graph a Parabola
Graph each equation.
A. y = 2(x – 1)2 – 5
y = 2(x – 1)2 – 5
Use the standard form of a parabola to find the vertex (h, k).
(1, –5)
Plot the vertex.
The graph points up and is narrow.
a = 2
Example 3

19. Analyze and Graph a Parabola
Sketch the graph.
Answer:
Example 3

20. Use the standard form of a parabola to find the vertex (h, k).
Analyze and Graph a Parabola
Graph each equation.
B. –(x – 3) = (y – 2)2
–(x – 3) = (y – 2)2
Use the standard form of a parabola to find the vertex (h, k).
(3, 2)
Plot the vertex.
Example 3

21. a = –1 The graph points left. Sketch the graph. Answer:
Analyze and Graph a Parabola
a = –1
The graph points left.
Sketch the graph.
Answer:
Example 3