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Graphing Quadratic Functions in Standard Form

Graphing Quadratic Functions in Standard Form. y = ax 2 + bx + c. y. Vertex (Maximum). x. Vertex (Minimum). Quadratic Functions. The graph of a quadratic function is a parabola. A parabola can open up or down.

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Graphing Quadratic Functions in Standard Form

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  1. Graphing Quadratic Functionsin Standard Form y = ax2 + bx + c

  2. y Vertex (Maximum) x Vertex (Minimum) Quadratic Functions The graph of a quadratic function is a parabola. A parabola can open up or down. If the parabola opens up, the lowest point (minimum) is called the vertex. If the parabola opens down, the vertex is the highest point (maximum). NOTE: if the parabola opened left or right it would not be a function!

  3. y a > 0 x a < 0 Standard Form The standard form of a quadratic function is y = ax2 + bx + c The parabola will open up when the a value is positive. The parabola will open down when the a value is negative.

  4. Line of Symmetry y x Line of Symmetry Parabolas have a symmetric property to them. If we drew a line down the middle of the parabola, we could fold the parabola in half. We call this line the line of symmetry. The line of symmetry ALWAYS passes through the vertex.

  5. Finding the Line of Symmetry When a quadratic function is in standard form For example… Find the line of symmetry of y = 3x2 – 18x + 7 y = ax2 + bx + c, The equation of the line of symmetry is This is best read as … the opposite of b divided by the quantity of 2 times a.

  6. Finding the Vertex For example, Find the vertex y = –2x2 + 8x –3 We know the line of symmetry always goes through the vertex. Thus, the line of symmetry gives us the x – coordinate of the vertex. To find the y – coordinate of the vertex, we need to plug the x – value into the original equation.

  7. A Quadratic Function in Standard Form The standard form of a quadratic function is given by y = ax2 + bx + c STEP 1: Find the line of symmetry STEP 2: Find the vertex STEP 3: Make a table of values using x values close to the line of symmetry. (Put the vertex in the middle of your table of values.)

  8. y x A Quadratic Function in Standard Form • Example 1 • a. Graph • Find and label the axis of symmetry. • Find the maximum/minimum • Find the domain & range • y = 2x2 – 4x – 1

  9. y x A Quadratic Function in Standard Form • Example 2 • a. Graph • Find and label the axis of symmetry. • Find the maximum/minimum • Find the domain & range • y = x2 - 2x – 1

  10. y x A Quadratic Function in Standard Form • Example 3 • a. Graph • Find and label the axis of symmetry. • Find the maximum/minimum • Find the domain & range • y = -1/6x2 – x – 3

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