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Graph y = ax²+b

Graph y = ax²+b. Vocabulary. Quadratic Equation – Equation in the form y=ax 2 + bx + c. Parabola – The general shape of a quadratic equation. It is in the form of a “U” which may open upward or downward. Graph Using a “T”-table.

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Graph y = ax²+b

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  1. Graph y = ax²+b

  2. Vocabulary • Quadratic Equation – Equation in the form y=ax2 + bx + c. • Parabola – The general shape of a quadratic equation. It is in the form of a “U” which may open upward or downward.

  3. Graph Using a “T”-table The most basic quadratic function in the family of quadratic functions, called the parent quadratic function, is y = x². x y -2 4 -1 1 y = x² 0 0 1 1 2 4

  4. Axis of symmetry – The line passing through the vertex and divides the parabola into two symmetric parts. (0,0) • Vertex – The maximum or minimum point of a parabola. The vertex of y = x² is (0,0).

  5. Example 1 Graph y = 3x2. Compare the graph with the graph of y = x2. STEP 1 Make a table of values for y =3x2. STEP 2 Plot the points from the table.

  6. Example 1 STEP 3 Draw a smooth curve through the points. STEP 4 Compare the graphs of y = 3x2and y = x2. Both graphs open up and have the same vertex, (0, 0), and axis of symmetry, x = 0. The graph of y = 3x2 is narrower than the graph of y =x2 because the graph of y = 3x2 is a vertical stretch (by a factor of 3) of the graph of y =x2.

  7. – x2. Graph y= Compare the graph with the graph of 1 1 y = x2. 4 4 – x2. Make a table of values for y = Example 2 STEP 1 STEP 2 Plot the points from the table.

  8. 1 1 1 4 4 4 1 – Both graphs have the same vertex (0, 0), and the same axis of symmetry, x = 0. However, the graph of x2 4 – – x2 x2 Compare the graphs ofy = is wider than the graph of y =x2 and it opens down. This is because the graph of andy =x2. is a vertical shrink with a reflection in the x-axis of the graph of y =x2. by a factor of y = y = Example 2 STEP 3 Draw a smooth curve through the points. STEP 4

  9. 2. y = x2 ANSWER 1 3 Your Turn Graph the function. Compare thegraph with the graph ofx2.

  10. ANSWER Your Turn Graph the function. Compare thegraph with the graph ofx2. 3. y =x2 +2

  11. Summary for ax2 • When a is positive, the parabola opens upward. • When a is negative, the parabola opens downward. • When a is larger than 1, the graph will be narrower than the graph of x2. • When a is less than 1, the graph will be wider (broader) than the graph of x2.

  12. Graph y = ax²+b

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