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is theminimum valueoff.The parabola opens down if; the vertex is a maximum point andf-b2a!is themaximum valueoff.56
They-intercept is the value offatx= 0. That is, they-intercept isThex-intercepts, if any, are found by solving the quadratic equationax2+bx+c= 0.Recall theQuadratic Formula.x=If the discriminantb2-4ac >0, the graph hasIf the discriminantb2-4ac= 0, the graph hasIf the discriminantb2-4ac= 0, the graph will touch thex-axis at itsIf the discriminantb2-4ac <0, the graph hasWhen the quadratic function is in the form:f(x) =a(x-h)2+k, we can use what welearned abouttransformationsin Sec 3.5 to identify the vertex.his theshift andkis theshift.Thevertexis.In this form, it is still true that ifa >0 the parabola opensandifa <0 the parabola opens.Recall, again,Section 2.2.They-intercept is the value offatx= 0. That is, they-intercept =f(0).You must calculate it.Thex-intercepts, if any, are found by lettingy= 0. That is, thex-intercepts, if any, are found bysolving the quadratic equationa(x-h)2+k= 0.RecallSection 1.2.This equation is best solved by theSquare-root Property.Do not.***************SummaryStandard Form(h, k) Formf(x) =ax2+bx+cf(x) =a(x-h)2+kvertex-b2a, f-b2a!!(h, k)aa >0 opens upsamea <0 opens downsamey-intletx= 0, solve forysamey-int=ccalculate they-interceptx-int(s)lety= 0, solve forxsame(factor or quad. formula)(use square-root property)57
Match each function with one of the graphs below.f(x) =-x2-1f(x) = (x+ 1)2-1f(x) =x2-2xf(x) =x2+ 2x+ 1f(x) =x2+ 2x+ 2xy1xy1-11-1xy1xy1xy158
Graph the functionf(x) = (x-3)2-10by starting with the graph ofy=x2and usingtransformations (shifting, compressing, stretching, and/or reflecting.)xyGraph each quadratic function by determining whether its graph opens up or down andby finding its vertex, axis of symmetry,y-intercept, and anyx-intercepts. Determinethe domain and range.Determine where the function is increasing and where it isdecreasing.f(x) =-x2+4xf(x) = (x+2)2-4f(x) =x2+6x+9xyxyxy59
f(x) =-3x2+ 3x-2f(x) = 2x2+ 5x+ 3xyxyDetermine, without graphing, whether the given quadratic function has a maximumvalue or a minimum value, and then find the value.f(x) = 4x2-8x+ 3f(x) =-3x2+ 12x+ 1f(x) = (x-3)2+ 5f(x) =-2(x+ 3)2-7Determine, without graphing, the interval on which the given function is increasingand on which it is decreasing.f(x) = 4x2-8x+ 3f(x) =-3x2+ 12x+ 1f(x) = (x-3)2+ 5f(x) =-2(x+ 3)2-760
The John Deere company has found that the revenue, in dollars, from sales of ridingmowers is a function of the unit pricep, in dollars, that it charges.If the revenueRisR(p) =-12p2+ 1900pwhat unit pricepshould be charged to maximize revenue? What is themaximum revenue?The marginal costC(in dollars) of manufacturingxcell phones (in thousands) is givenbyC(x) = 5x2-200x+ 4000.How many cell phones should be manufactured to minimize themarginal cost? What is the minimal marginal cost?