4 Section 10.2 “Graph y = ax² + bx + c” Properties of the Graph of a Quadratic Functiony = ax² + bx + c is a parabola that:-opens up if a > 0-opens down if a < 0-is narrower than y = x² if the |a| > 1-is wider than y = x² if the |a| < 1-has an axis of x = -(b/2a)-has a vertex with an x-coordinate of -(b/2a)-has a y-intercept of c. So the point (0,c) is on the parabola
5 Finding the Axis of Symmetry and the Vertex of a Parabola Consider the graph y = -2x² + 12x – 7(a) Find the axis of symmetry of the graph(b) Find the vertex of the graphAxis of symmetry:Substitutea = -2b = 12Substitute the x-value into the original equation and solve for y.The vertex of the parabolais the point (3,11)
6 Graph y = 3x² - 6x + 2 Step 1: Determine if parabola opens up or down Step 2: Find and draw theaxis of symmetryStep 3: Find and plot the vertexStep 4: Plot two points. Choose two x-values less than the x-coordinate of the vertex. Then find the corresponding y-values.xy2-111Step 5: Reflect the points plotted over the axis of symmetry.Step 6: Draw a parabola through the plotted points.Minimum Value
7 Graph y = -1/4x² - x + 1 Step 1: Determine if parabola opens up or downDOWNStep 2: Find and draw theaxis of symmetryStep 3: Find and plot the vertexStep 4: Plot two points. Choose two x-values more than the x-coordinate of the vertex. Then find the corresponding y-values.xy12-2Step 5: Reflect the points plotted over the axis of symmetry.Maximum ValueStep 6: Draw a parabola through the plotted points.
8 Minimum and Maximum Values For y = ax² + bx + c, the y-coordinate of the vertex is the MINIMUM VALUE of the function if a > 0 or the MAXIMUM VALUE of the function if a < 0.y = ax² + bx + c; a > 0y = -ax² + bx + c; a < 0maximumminimum
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