Parabolas

Graphing Parabolas Standard Form of a Quadratic Function y=ax2+bx+c when a≠0 Find the vertex Minimum Maximum Find the y-intercept

Properties y=ax2+bx+c When a>0 parabola opens up When a<0 parabola opens down Axis of symmetry is x=-b/2a Vertex x coordinate is –b/2a y coordinate is found by substituting the x coordinate into the function y-intercept is (0,c)

To Graph Find and graph the axis of symmetry Find and graph the vertex Find and graph the y-intercept Find and graph at least one other point on both sides of the axis of symmetry Zero’s (x-intercepts) can be used Sketch the curve

Ex1: y=x2-2x-3 axis of symmetry Other Points The vertex Sketch the curve y-intercept

Ex 2: y=-6x2-12x-1 Axis of symmetry Vertex y-intercept Two points (-1, 5) y-intercept (0,-1) Two points (-1.91,0) (-.09,0) Sketch the curve

Ex 3: y=-4x2-24x-36 Axis of symmetry Vertex y-intercept Two points (-3, 0) y-intercept (0, -36) Two points (-2,-4) (-4,-4) Sketch the curve

Translating Parabolas

Vertex Form y=a(x-h)2+k h is how many the function has been translated horizontally k is how many the function has been translated vertically Vertex is (h,k) Line of symmetry is x=h

Writing Equations in Vertex Form A parabola has a vertex at (3,4) with the point (5, -4) on the parabola h=3, k=4 Find a y=a(x-h)2+k y=-2(x-3)2+4 -4=a(5-3)2+4 -4=4a+4 -8=4a a=-2

Converting to Vertex Form Find the line of symmetry (aka the x coordinate of the vertex) Find the y coordinate of the vertex Substitute into the vertex form equations y=a(x-h)2+k

Ex: -3x2+12x+5 h = x= -12/2(-3) = -12/-6 = 2 k = y= -3(2)2+12(2)+5 = -12+24+5 =17 y=a(x-h)2+k y=-3(x-2)2+17

Practice Problems P. 58 Choose 3 from # 1-9 Only find the vertex and state if it is a minimum or maximum Choose 4 from # 21-29 P. 60 Choose 3 from # 1-6 Choose 3 from #7-12 Choose 4 from #19-27