3 Forms Of A Quadratic Function

3 Forms Of A Quadratic Function

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  3 Forms ofa Quadratic Function!
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  Key IdeasThe axisof symmetry divides the parabola into mirror images and passes through the vertex.
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  a tells whetherthe graph opens up or down and whether the graph is wide or narrow.
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  H controls horizontaltranslations.
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  K controls verticaltranslations
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  a>0; the graphopens up.
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  a<0; the graphopens down.Standard Formf(x) = ax^2 + bx + c
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  Y=2x^2-8x+6Step 2: Find the vertex: x= -b/2a= -(-8)/2(2) X = 2 y= 2(2)^2-8(2)+6 y = -2Step 1: Identify coefficients: a=2 b=-8 c=6 a>0 so the parabola opens upStep 4: Plot 2 more points. Go to the left by one and up 2. Then do it again for the right side.Step 3: Draw axis of symmetry x=-b/2a x=2Step 5: Draw parabola through the points.Step 6: Label the points(3,0)(1,0)(2,-2)
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  Vertex Formf(x) =a (x-h)^2 + k
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  Y=2(x-3)^2-3Step 3: Plot 2 more points. Go to the left by one and up 2. Then do it again for the right side.Step 1: Determine vertex: (h,k)= (3, -3)Step 4: Connect the points to form a parabola.Step 2: Plot the vertex, (3,-3) Draw the axis of symmetry. x=h so x=3Step 5: Label the points(4,-1)(2,-1)(3,-3)
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  Intercept Formf(x) =a (x-p) (x-q)
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  Y= 2(x-3)(x+1)(-1,0)(3,0)Step 2: Find the coordinates of the vertex and plot them. ((p+q)/2, f(p+q)/2) x= (3-1)/2= 2/2=1 x=1 Y= 2(1-3)(1+1) Y= 2(-2)(2) y=-8 Vertex= (1,-8)Step 3: Plot the axis of symmetry. Axis of symmetry is x=(p+q)/2 x=1Step 1: Plot x-intercepts x=3 and x=-1Step 5: Label the points.Step 4: Connect the points.(1,-8)