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2.10 2 Graph y = ax + c 2.10-2.11 Quiz: Friday Midterm: March 11 Vocabulary • A quadratic function is a nonlinear (not a line) function that can be written in the standard form y = ax2+ bx + c where a ≠ 0 • Every quadratic function has a U-shaped graph called a parabola. Vocabulary • The most basic quadratic function in the family of quadratic functions, called the parent quadratic function, is y = x2 X -2 Y= 4 -1 0 1 2 1 0 1 4 Parts of a Parabola • The lowest or highest point on a parabola is the vertex. • The line that passes through the vertex and divides the parabola into two symmetric parts is called the axis of symmetry. Graph y = ax2 • The coefficient “a” can stretch or shrink the graph. • If “a” is negative then the graph flips upside down. (Or as I like to call it…makes a SAD face) Example 1: • Graph y = 2x2. Compare the graph with the parent function, y = x2. – You need to make a table of values. X Y= -2 -1 0 1 2 You Try: • Graph y = 1/2x2. Compare the graph with the parent function, y = x2. X -2 -1 0 1 Y= 2 Example 2: • Graph y = -3x2. Compare the graph with the parent function, y = x2. – You need to make a table of values. X Y= -2 -1 0 1 2 Graph y = ax2 + c • The constant “c” moves the graph up or down. – If “c” is positive it moves the graph up – if “c” is negative it moves the graph down. Example 4: • Graph y = x2 + 2. Compare the graph with the parent function, y = x2. – You need to make a table of values. X Y= -2 -1 0 1 2 You Try: • Graph y = x2 – 4. Compare the graph with the parent function, y = x2. Homework: • P. 100 # 1-9all, 16, 17, 20, 21