Warm-Up Exercises 1. Identify the axis of symmetry for the graph of y = 3x 2. ANSWER x = 0 2. Identify the vertex of the graph of y = 3x 2. ANSWER (0,

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Presentation transcript:

Warm-Up Exercises 1. Identify the axis of symmetry for the graph of y = 3x 2. ANSWER x = 0 2. Identify the vertex of the graph of y = 3x 2. ANSWER (0, 0)

Warm-Up Exercises ANSWER 1. Graph x 2 = – 8y. Identify the focus, directrix, and axis of symmetry. Ex: For Your Notes

Warm-Up Exercises 2. Write an equation of the parabola shown. ANSWER y 2 = 12x Ex: For Your Notes

Warm-Up Exercises EXAMPLE 1 Graph an equation of a parabola SOLUTION STEP 1 Rewrite the equation in standard form. Write original equation Graph x = – y 2. Identify the focus, directrix, and axis of symmetry. – 8x = y 2 Multiply each side by – x = – y2y2

Warm-Up Exercises EXAMPLE 1 Graph an equation of a parabola STEP 2 Identify the focus, directrix, and axis of symmetry. The equation has the form y 2 = 4px where p = – 2. The focus is (p, 0), or (– 2, 0). The directrix is x = – p, or x = 2. Because y is squared, the axis of symmetry is the x - axis. STEP 3 Draw the parabola by making a table of values and plotting points. Because p < 0, the parabola opens to the left. So, use only negative x - values.

Warm-Up Exercises EXAMPLE 1 Graph an equation of a parabola

Warm-Up Exercises EXAMPLE 2 Write an equation of a parabola SOLUTION x 2 = 4py Standard form, vertical axis of symmetry x 2 = 4 y 3232 Substitute for p 3232 x 2 = 6y Simplify. Write an equation of the parabola shown. The graph shows that the vertex is (0, 0) and the directrix is y = – p =. Substitute for p in the standard form of the equation of a parabola – 3232

Warm-Up Exercises GUIDED PRACTICE for Examples 1 and 2 Graph the equation. Identify the focus, directrix, and axis of symmetry of the parabola. 1. y 2 = –6x ANSWER The axis of symmetry is the x -axis. x =. 3 2 The directrix is 3 2 The focus is (–, 0).

Warm-Up Exercises GUIDED PRACTICE for Examples 1 and 2 Graph the equation. Identify the focus, directrix, and axis of symmetry of the parabola. 2. x 2 = 2y y = – The directrix is The focus is The axis of symmetry is x = ANSWER 0,

Warm-Up Exercises GUIDED PRACTICE for Examples 1 and 2 Graph the equation. Identify the focus, directrix, and axis of symmetry of the parabola. 3. y = – x ANSWER The focus is (0, –1). The directrix is y = 1. The axis of symmetry is x = 0.

Warm-Up Exercises GUIDED PRACTICE for Examples 1 and 2 Graph the equation. Identify the focus, directrix, and axis of symmetry of the parabola. 4. x = – y , 0 x = – The directrix is The focus is The axis of symmetry is y = ANSWER

Warm-Up Exercises GUIDED PRACTICE for Examples 1 and 2 Write the standard form of the equation of the parabola with vertex at (0, 0) and the given directrix or focus. 5. Directrix: y = 2 x 2 = – 8y ANSWER 6. Directrix: x = 4 y 2 = – 16x ANSWER

Warm-Up Exercises GUIDED PRACTICE for Examples 1 and 2 Write the standard form of the equation of the parabola with vertex at (0, 0) and the given directrix or focus. 7. Focus: (–2, 0) y 2 = – 8x ANSWER 8. Focus: (0, 3) x 2 = 12y ANSWER