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Vertex and Intercept Form of Quadratic Function. Standard: MM2A3c Students will Investigate and explain characteristics of quadratic functions, including domain, range, vertex, axis of symmetry, zeros, intercepts, extrema , intervals of increase, and decrease, and rates of change .

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## Vertex and Intercept Form of Quadratic Function

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**Vertex and Intercept Form of Quadratic Function**Standard: MM2A3c Students will Investigate and explain characteristics of quadratic functions, including domain, range, vertex, axis of symmetry, zeros, intercepts, extrema, intervals of increase, and decrease, and rates of change.**Vertex Form of the Quadratic**Determine the vertex of the following functions: f(x) = 2(x – 1)2 + 1 g(x) = -(x + 3)2 + 5 h(x) = 3(x – 2)2 – 7**Vertex & Axis of Symmetry Summary**• Put equation in standard form f(x) = ax2 + bx + c • Determine the value “a” and “b” • Determine if the graph opens up (a > 0) or down (a < 0) • Find the axis of symmetry: • Find the vertex by substituting the “x” into the function and solving for “y” • Determine two more points on the same side of the axis of symmetry • Graph the axis of symmetry, vertex, & points**Vertex Form of the Quadratic**V = (1, 1) V = (-3, 5) V = (2, -7) Determine the vertex of the following equations: f(x) = 2(x – 1)2 + 1 g(x) = -(x + 3)2 + 5 h(x) = 3(x – 2)2 – 7 Compare the equations and the vertices. Do you notice a pattern? The x part is the opposite sign of the number inside the brackets and the y part is the same as the number added or subtracted at the end.**Vertex Form of the Quadratic**• The vertex form of the quadratic equation is of the form: • y = a(x – h)2 + k, where: • The vertex is located at (h, k) • The axis of symmetry is x = h • The “a” is the same as in the standard form • The “a” is the stretch of the function • The vertex is shifted right by h • The vertex is shifted up by k**Vertex Form of the Quadratic**From y = x2 Stretch factor Vertex Shift VERTICAL amount y = a(x – h)2 + k Vertex Shift HORIZONTAL amount**In Class:**• Do page 63 of Note Taking Guide • Do first 6 problems of Henley Task Day 2 – be sure to graph the y = x2 for each graph.**In Class**• Do page 64 of the Note Taking Guide • Do Day 2 of the Henley Task, # 4a – 4e all**Intercept Form of the Quadratic Function**V = (2, -1) V = (-2.5, -4.5) How can we determine the vertex of the following equations without putting them in standard form? f(x) = (x – 3)(x – 1) g(x) = 2(x + 1)(x + 4) h(x) = -3(x – 2)(x + 3) Determine the x-intercepts (zero prod rule) Find the axis of symmetry (average) Find “y” value of the vertex (sub into f(x)) V = (-0.5, 18.75)**Homework**• Page 65, # 1, 2, and 19 – 22 all**Convert from Standard to Vertex Form**• Standard: MM2A3a Students will • Convert between standard and vertex form.**Convert from Standard to Vertex Forms**• We converted from Vertex form to Standard form of the quadratic function above in slide 3 by expanding the (a – h)2 term and combining like terms • How can we convert from Standard form to Vertex form?**Convert from Standard to Vertex Forms**• Look at the standard form: y = ax2 + bx + c, where a ≠ 0 • And look at the Vertex form: y = a(x – h)2 + k • “h” is the axis of symmetry, which is the “x” part of the coordinates of the vertex • “k” is the “y” part of the vertex**Convert from Standard to Vertex Forms**• How did we find the axis of symmetry? • This is the “h” of the vertex form • How did we then find the “y” part of the vertex? • Substitute the x into the original equation and solve for y. • This is the “k” of the vertex form • The “a” is the same for both forms**Convert from Standard to Vertex Forms**• Convert the following functions to vertex form: • f(x) = x2 + 10x – 20 • y = (x + 5)2 - 45 • g(x) = -3x2 – 3x + 10 • y = -3(x + 0.5)2 + 10.75 • h(x) = 0.5x2 – 4x – 3 • y = 0.5(x – 4)2 - 11

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