Key Words quadratic function parabola vertex axis of symmetry monomial binomial

Graph a Quadratic Function Using a Table Example 1 Graph y = 2 1 x 2x – STEP 1 Make a table of values for y Choose values of x on both sides of the axis of symmetry x 0. = 2 1 x 2x – = SOLUTION The function y is in standard form. Because b 0, you know that the axis of symmetry is x 0. = 2 1 x 2x 2 1 – = = x 2x 2 a y = +c

Graph a Quadratic Function Using a Table Example 1 y 1 x – 1 – 2 – STEP 2 Plot the points from the table. STEP 3 Draw a smooth curve through the points.

Checkpoint Graph a Quadratic Function Using a Table Graph the function using a table of values. ANSWER 1. y = – 3 x 2x 2

Checkpoint Graph a Quadratic Function Using a Table Graph the function using a table of values. ANSWER 2. y = – x 2x 2 – 2

Checkpoint Graph a Quadratic Function Using a Table Graph the function using a table of values. ANSWER 3. y = 4 1 x 2x 2 3 +

Graph a Quadratic Function in Standard Form Example 2 Graph =x 2x 2 6x6xy5+ – SOLUTION The function is in standard form y ax 2 bx c where a 1, b 6, and c 5. Because a > 0, the parabola opens up. = ++ == – = STEP 1Draw the axis of symmetry. STEP 2Find and plot the vertex. The x -coordinate of the vertex is 3. Find the y -coordinate.. = 3x 2a2a b – = – 2 () 1 = 6 –

Graph a Quadratic Function in Standard Form Example 2 =x 2x 2 6x6xy5+ – = 65+ – ()2)2 3 () 3 = 4 – The vertex is. () 3, 4 – =x 2x 2 6x6xy5+ – =x 2x 2 6x6xy5+ – = 5+ – ()2)2 0 6 () 0 = 5 = 5+ – ()2)2 1 6 () 1 = 0 STEP 3Plot two points to the left of the axis of symmetry. Evaluate the function for two x -values that are less than 3, such as 0 and 1.

Graph a Quadratic Function in Standard Form Example 2 Plot the points and. Plot their mirror images by counting the distance to the axis of symmetry and then counting the same distance beyond the axis of symmetry. () 0, 5 () 1, 0 STEP 4Draw a parabola through the points.

Checkpoint Graph a Quadratic Function in Standard Form Graph the function. Label the vertex and the axis of symmetry. 4. = x 2x 2 6x6xy2 +– ANSWER

Checkpoint Graph a Quadratic Function in Standard Form Graph the function. Label the vertex and the axis of symmetry. ANSWER 5. = x 2x 2 2x2xy1 –– +

Checkpoint Graph a Quadratic Function in Standard Form Graph the function. Label the vertex and the axis of symmetry. ANSWER 6. = 2x 22x 2 xy1 – +

Example 3 Multiply Binomials Find the product. () 3+2x2x () 7x – Write products of terms. SOLUTION () 7 – () 3+2x2x () 7x – = 2x2x () x+2x2x+3x3x+3 () 7 – = 2x 22x 2 14x+3x3x – 21 – Multiply. = 2x 22x 2 11x – 21 – Combine like terms.

Checkpoint Multiply Binomials Find the product. 7. () 4x – () 6x + ANSWER x 2x 2 +2x2x 24 – 8. () 1x – () 13x3x + ANSWER 3x 23x 2 2x2x 1 –– 9. – () 52x2x () 2x – ANSWER 2x 22x 2 9x9x 10 – +

Example 4 Write a Quadratic Function in Standard Form Write the function in standard form. Write original function. SOLUTION ()2)2 2x – y = 25+ ()2)2 2x – y = 25+ () 2x – = 25+ () 2x – Rewrite as. ()2)2 2x – () 2x – () 2x – () 2x2xx 2x 2 – = 24+2x2x – 5+ Multiply using FOIL. () 4x4xx 2x 2 – = Combine like terms. 8x8x2x 22x 2 – = 8+5+ Use the distributive property. 8x8x2x 22x 2 – = 13+ Combine like terms.

Checkpoint Write a Quadratic Function in Standard Form Write the function in standard form. 10. () 3x – () 1x + y = () 6x – y = 3 () 4x – 12. ()2)2 1x – y = 3 –– ANSWER 2x 22x 2 4x4x 6 –– y = y = 3x 23x 2 30x 72 – + ANSWER y = x 2x 2 2x2x 4 – + –