How do you find its vertex, axis of symmetry, y-intercept and x-intercept for f(x)=−3x2+3x−2?

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jojoann325 · Accepted Answer

Step 1 xofvertexPSK=x of axis of symmetry: x=(−b2a)=−3−6=12 y of vertex: y=f(12)=−34+32−2=−54 y intercept: y=−2 x-intercept: →y=0 D=b2−4c=9−24=−15&amp;lt;0 There are no real roots (no x-intercepts) because D&amp;lt;0 Since a&amp;lt;0, the parabola opens downward. The parabola is completely below the x-axis.

Jason Duke · Accepted Answer

Step 1  f(x)=−3x2+3x−2  The general formula for a quadratic equation is ax2+bx+c  a=−3  b=3  The graph of a quadratic equation is a parabola. A parabola has an axis of symmetry and a vertex. The axis of symmetry is a vertical line the divides the parabola into to equal halves. The line of symmetry is determined by the equation  x=−b2a  The vertex is the point where the parabola crosses its axis of symmetry, and is defined as a point (x,y)  Axis of Symmetry  x=−b2a=−32(−3)=−3−6=12  The axis of symmetry is the line x=12  Vertex  Determine the value for y by substituting y for f(x) and by substituting 12 for x in the equation,  y=−3x2+3x−2  y=−3(12)2+3(12)−2  y=−3(14)+32−2S  y=−34+32−2  The common denominator is 8  y=−34×22+32×44−2×88=  y=−68+128−168=  y=−108  y=−54  The vertex is (x, y)=(12, −54)  X-intercept  The x-intercepts are where the parabola crosses the x-axis.There are no x-intercepts for this equation because the vertex is below the x-axis and the parabola is facing downward.  Y-intercept  The y-intercept is where the parabola crosses the y-axis. To find the y-intercept, make x=0, and solve the equation for y.  y=−3(0)2+3(0)−2=  y=−2  The y-intercept is -2  graph {y=−3x2+3x−2[−14, 14.47, −13.1, 1.14]}

How do you find its vertex, axis of symmetry, y-intercept

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