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Sketch the graph of the function. Leave the function in the gve points (the vertex is a necessary points that you need to find). State the vertex and points that fit on the graph. Use the normal movement of a parabola and stretch 0 to find the remaining points after you have found the vertex. Show all work. y=-3x^(2)+6x+5

Sketch the graph of the function. Leave the function in the gve points (the vertex is a necessary points that you need to find). State the vertex and points that fit on the graph. Use the normal movement of a parabola and stretch 00 to find the remaining points after you have found the vertex. Show all work.\newline11) y=−3x2+6x+5 y=-3 x^{2}+6 x+5

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Full solution

Q. Sketch the graph of the function. Leave the function in the gve points (the vertex is a necessary points that you need to find). State the vertex and points that fit on the graph. Use the normal movement of a parabola and stretch 00 to find the remaining points after you have found the vertex. Show all work.\newline11) y=−3x2+6x+5 y=-3 x^{2}+6 x+5
  1. Find Vertex: Find the vertex of the parabola using the formula for the x-coordinate of the vertex, x=−b2ax = -\frac{b}{2a}.\newlineFor the given function y=−3x2+6x+5y = -3x^2 + 6x + 5, a=−3a = -3 and b=6b = 6.\newlinex=−62∗(−3)=−6−6=1x = -\frac{6}{2*(-3)} = -\frac{6}{-6} = 1.
  2. Calculate Y-Coordinate: Calculate the y-coordinate of the vertex by substituting x=1x = 1 into the function.y=−3(1)2+6(1)+5=−3+6+5=8.y = -3(1)^2 + 6(1) + 5 = -3 + 6 + 5 = 8.Vertex is at (1,8)(1, 8).
  3. Plot Vertex: Plot the vertex (1,8)(1, 8) on the graph.
  4. Use Symmetry: Use the symmetry of the parabola to find another point.\newlineSince the parabola is symmetric about the vertex, choose x=0x = 0 to find the y-intercept.\newliney=−3(0)2+6(0)+5=5y = -3(0)^2 + 6(0) + 5 = 5.\newlinePoint (0,5)(0, 5) is on the graph.
  5. Plot Points: Plot the point (0,5)(0, 5) and its symmetric point (2,5)(2, 5) on the graph.
  6. Plot Points: Plot the point (0,5)(0, 5) and its symmetric point (2,5)(2, 5) on the graph.Use the stretch factor of 00 to find additional points.\newlineThis is incorrect; the stretch factor is not 00, it is −3-3.

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