Presentation on theme: "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."— Presentation transcript:
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.
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