Presentation on theme: "2.1 Quadratic Functions Use the graphing calculator and graph y = x2"— Presentation transcript:
12.1Quadratic FunctionsUse the graphing calculatorand graph y = x2y = 2x2y =The quadratic function f(x) = a(x – h)2 + kis said to be in standard form. Vertex (h,k)If a > 0, opens up. If a < 0, opens down.
2Ex. Write the quadratic function in standard form, find the vertex, identify the x-int.’sand sketch. f(x) = 2x2 + 8x + 7f(x) = 2x2 + 8x + 7Factor out a 2 from the x’sf(x) = 2(x2 + 4x ) + 7+ 4- 8Complete the squaref(x) = 2(x + 2)2 - 1V( , )Up or DownTake the original and set = 0 to find the x-int.0 = 2x2 + 8x + 7Use quad. formula on calc.x = ,Now sketch it.
4Ex. Sketch the graph of f(x) = -x2 + 6x - 8 Factor -1 out of the x termsf(x) = -(x2 – 6x ) - 8+ 9+ 9Complete the squaref(x) = -(x – 3)2 + 1V(3, 1)Down
5To find a vertex of the quadratic f(x) = ax2 + bx + c, (without putting the equation into standard form),evaluate by lettingEx. P = .0014x xy = 1.68
6Find the the equations of a parabola that cups up and down given the x-intercepts (1, 0) and (-3, 0).First, write the x-intercepts as factors.y = (x - 1)(x + 3)The parabola that cups up is y = x2 + 2x - 3The parabola that cups down requires a negativein front of the quadratic.y = -(x2 + 2x - 3)or y = -x2 - 2x + 3
7Given the vertex and point on a given parabola, find the standard equation of the parabola.V(4, -1); point (2, 3)Fill in the points in the standard parabola formy = a(x - h)2 + k and solve for a.3 = a(2 - 4)2 + (-1)3 = 4a -14 = 4a1 = aThe answer isy = 1(x - 4)2 - 1