\begin{tabular}{|l|l|}\hline You get this: & Fill in this: \\\hliney=−x2−6x+16 & Either form of the equation other than standard form: \\\cline { 1 - 2 } & Vertex of the parabola: \\\cline { 2 - 2 } & x-intercepts and y-intercept: \\\hline\end{tabular}
Q. \begin{tabular}{|l|l|}\hline You get this: & Fill in this: \\\hliney=−x2−6x+16 & Either form of the equation other than standard form: \\\cline { 1 - 2 } & Vertex of the parabola: \\\cline { 2 - 2 } & x-intercepts and y-intercept: \\\hline\end{tabular}
Factor Out −1: Factor out −1 from the x terms in the equation y=−x2−6x+16.y=−1(x2+6x)+16
Find Value: Find the value of (2b)2 for x2+6x to complete the square.Coefficient of x is 6.(26)2=32=9
Add and Subtract: Add and subtract 9 inside the parentheses to complete the square.y=−1(x2+6x+9−9)+16
Rewrite Equation: Rewrite the equation showing the perfect square trinomial and the constant term.y=−1((x+3)2−9)+16
Distribute and Simplify: Distribute the −1 and simplify the equation.y=−(x+3)2+9+16y=−(x+3)2+25
Identify Vertex: Identify the vertex from the vertex form equation y=−(x+3)2+25.Vertex is (−3,25).
Find X-Intercepts: Find the x-intercepts by setting y to 0 and solving for x.0=−(x+3)2+25(x+3)2=25x+3=±5x=−3±5x-intercepts are (−8,0) and (2,0).
Find Y-Intercept: Find the y-intercept by setting x to 0 in the original equation.y=−02−6(0)+16y=16y-intercept is (0,16).
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