Day 4: Graph y = a(x – h)2 + k Part 1 1. How can you tell if a parabola opens up or down? 2. The _______________ is the highest or lowest point on the graph of a parabola. 3. When a quadratic equation is in the form y= a(x-h)2 + k, we call this vertex form. This is because it is easy to determine the coordinates of the vertex of the parabola. The vertex is ____________ when the equation is in vertex form y= a(x-h)2 + k. 4. The “centre line” of each parabola is called its ____________ of _________________. 5. The ____________________ always lies on the axis of symmetry. 6. The points where the parabola crosses the x-axis are called the x-intercepts or _________ of the relation. Summary of Graphing Equations in Vertex Form y= a(x-h)2 + k Operation Resulting Equation Multiply by a y = ax2 Replace x by (x-h) Add k y= (x-h)2 y= x2 + k What happens If a > 0, parabola opens up. If a< 0, parabola opens down. This transformation is called a vertical reflection. If a > 1 or a< -1, parabola gets thinner This transformation is called a vertical stretch. If -1 < a < 1, parabola gets wider. This transformation is called a vertical compression. If h > 0 (“-“ in the brackets), parabola moves h units to the right. This transformation is called a horizontal translation. If h < 0 ( “+” in the brackets), parabola translates h units to the left. This transformation is called a horizontal translation. If k > 0, parabola moves k units up. This transformation is called a vertical translation. If h < 0, parabola moves k units down. This transformation is called a vertical translation. Example 1: Complete the chart. Function Direction of Opening Coordinates of Vertex Narrow or Wide? Equation of Axis of Symmetry Maximum or minimum value y= 3(x-1)2 + 2 y= -(x-4)2 + 1 1 (x+2)2 - 3 4 y= 2x2 + 4 y= - y= 4(x-5)2 Example 2: Graph each quadratic relation and fill in the chart. a) y = -x2 + 3 Property vertex Axis of symmetry Stretch or compression factor relative to y = x2 Direction of opening Values x may take Values y may take Note: The order of transformations follows the order of operations. Stretches, compressions and reflections are done before translations! 1 b) = 2 ( + 4)2 − 3 Property vertex Axis of symmetry Stretch or compression factor relative to y = x2 Direction of opening Values x may take Values y may take Example 3: Determine the equation of the given parabola. Example 4: Write an equation for the parabola with vertex (-4, 5), opening upward, 2 with a vertical compression factor of 5. Challenge: Page 188 #19, 20

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# Day 4 Vertex Form 1