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y=-x^(2)-6x+16
Either form of the equation other than standard form:



Vertex of the parabola:




x-intercepts and 
y-intercept:

\begin{tabular}{|l|l|}\newline\hline You get this: & Fill in this: \\\newline\hliney=x26x+16 y=-x^{2}-6 x+16 & Either form of the equation other than standard form: \\\newline\cline { 11 - 22 } & Vertex of the parabola: \\\newline\cline { 22 - 22 } & x x -intercepts and y y -intercept: \\\newline\hline\newline\end{tabular}

Full solution

Q. \begin{tabular}{|l|l|}\newline\hline You get this: & Fill in this: \\\newline\hliney=x26x+16 y=-x^{2}-6 x+16 & Either form of the equation other than standard form: \\\newline\cline { 11 - 22 } & Vertex of the parabola: \\\newline\cline { 22 - 22 } & x x -intercepts and y y -intercept: \\\newline\hline\newline\end{tabular}
  1. Factor Out 1-1: Factor out 1-1 from the xx terms in the equation y=x26x+16y = -x^2 - 6x + 16.\newliney=1(x2+6x)+16y = -1(x^2 + 6x) + 16
  2. Find Value: Find the value of (b2)2(\frac{b}{2})^2 for x2+6xx^2 + 6x to complete the square.\newlineCoefficient of xx is 66.\newline(62)2=32=9(\frac{6}{2})^2 = 3^2 = 9
  3. Add and Subtract: Add and subtract 99 inside the parentheses to complete the square.y=1(x2+6x+99)+16y = -1(x^2 + 6x + 9 - 9) + 16
  4. Rewrite Equation: Rewrite the equation showing the perfect square trinomial and the constant term.\newliney=1((x+3)29)+16y = -1((x + 3)^2 - 9) + 16
  5. Distribute and Simplify: Distribute the 1-1 and simplify the equation.\newliney=(x+3)2+9+16y = -(x + 3)^2 + 9 + 16\newliney=(x+3)2+25y = -(x + 3)^2 + 25
  6. Identify Vertex: Identify the vertex from the vertex form equation y=(x+3)2+25y = -(x + 3)^2 + 25.\newlineVertex is (3,25)(-3, 25).
  7. Find X-Intercepts: Find the x-intercepts by setting yy to 00 and solving for xx.0=(x+3)2+250 = -(x + 3)^2 + 25(x+3)2=25(x + 3)^2 = 25x+3=±5x + 3 = \pm5x=3±5x = -3 \pm 5x-intercepts are (8,0)(-8, 0) and (2,0)(2, 0).
  8. Find Y-Intercept: Find the y-intercept by setting xx to 00 in the original equation.\newliney=026(0)+16y = -0^2 - 6(0) + 16\newliney=16y = 16\newliney-intercept is (0,16)(0, 16).

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