WarmUp Exercises 1 Identify the axis of symmetry

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Warm-Up Exercises 1. Identify the axis of symmetry for the graph of y =

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

Warm-Up Ex: For Your. Exercises Notes 1. Graph x 2 = – 8 y.

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

Warm-Up Ex: For Your. Exercises Notes 2. Write an equation of the parabola shown.

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

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

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

Warm-Up 1 Exercises EXAMPLE Graph an equation of a parabola STEP 2 Identify the

Warm-Up 1 Exercises EXAMPLE Graph an equation of a parabola STEP 2 Identify the focus, directrix, and axis of symmetry. The equation has the form y 2 = 4 px 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 1 Exercises EXAMPLE Graph an equation of a parabola

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

Warm-Up 2 Exercises EXAMPLE Write an equation of a parabola Write an equation of

Warm-Up 2 Exercises EXAMPLE Write an equation of a parabola Write an equation of the parabola shown. SOLUTION The graph shows that the vertex is (0, 0) and the directrix is y = – p = – 32. Substitute 32 for p in the standard form of the equation of a parabola. x 2 = 4 py Standard form, vertical axis of symmetry 3 x 2 = 4 2 x 2 = 6 y y Substitute Simplify. 3 for p 2

Warm-Up Exercises GUIDED PRACTICE for Examples 1 and 2 Graph the equation. Identify the

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 = – 6 x ANSWER The focus is (– 3 , 0). 2 The directrix is x = 3. 2 The axis of symmetry is the x-axis.

Warm-Up Exercises GUIDED PRACTICE for Examples 1 and 2 Graph the equation. Identify the

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 = 2 y ANSWER 1. The directrix is y = – 1. 2 2 The axis of symmetry is x = 0. The focus is 0,

Warm-Up Exercises GUIDED PRACTICE for Examples 1 and 2 Graph the equation. Identify the

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 = – 1 x 2 4 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

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 2 4. x = – y 3 ANSWER 3, 0 The focus is 4 3 The directrix is x = –. 4 The axis of symmetry is y = 0.

Warm-Up Exercises GUIDED PRACTICE for Examples 1 and 2 Write the standard form of

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 ANSWER x 2 = – 8 y 6. Directrix: x = 4 ANSWER y 2 = – 16 x

Warm-Up Exercises GUIDED PRACTICE for Examples 1 and 2 Write the standard form of

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) ANSWER y 2 = – 8 x 8. Focus: (0, 3) ANSWER x 2 = 12 y