 # Chapter 9.1 Notes. Quadratic Function – An equation of the form ax 2 + bx + c, where a is not equal to 0. Parabola – The graph of a quadratic function.

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Chapter 9.1 Notes

Quadratic Function – An equation of the form ax 2 + bx + c, where a is not equal to 0. Parabola – The graph of a quadratic function. Axis of Symmetry – The vertical line containing the vertex of a parabola. Vertex – The maximum or minimum point of a parabola.

y = x 2 – x – 2 XY -2 0 1 2 3

y = x 2 + 2x + 3 A.B. C.D.

 -x 2 + 3x – 7  x 2 - 7x + 8  -3x 2 + 21x – 9

y = –2x 2 – 8x – 2

Graph the function f(x) = –x 2 + 5x – 2. Step 1Find the equation of the axis of symmetry. Formula for the equation of the axis of symmetry a = –1 and b = 5 Simplify. or 2.5

f(x)= –x 2 + 5x – 2Original equation Step 2Find the vertex, and determine whether it is a maximum or minimum. = 4.25Simplify. The vertex lies at (2.5, 4.25). Because a is negative the graph opens down, and the vertex is a maximum. = –(2.5) 2 + 5(2.5) – 2x = 2.5

f(x)= –x 2 + 5x – 2Original equation = –(0) 2 + 5(0) – 2x = 0 = –2Simplify. The y-intercept is –2. Step 3Find the y-intercept.

Step 4The axis of symmetry divides the parabola into two equal parts. So if there is a point on one side, there is a corresponding point on the other side that is the same distance from the axis of symmetry and has the same y-value.

Answer: Step 5Connect the points with a smooth curve.

x 2 + 2x – 3 Step 1: Axis of Symmetry Step 2: Vertex, Max or Min? Step 3: Y-intercept Step 4: Plot Points Step 5: Connect with Smooth Curve

1-12, 17-20

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