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A parabola opening up or down has vertex (0,0)(0,0) and passes through (8,−8)(8,-8). Write its equation in vertex form.\newlineSimplify any fractions.

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Q. A parabola opening up or down has vertex (0,0)(0,0) and passes through (8,−8)(8,-8). Write its equation in vertex form.\newlineSimplify any fractions.
  1. Identify Vertex Form: Identify the vertex form of a parabola.\newlineVertex form: y=a(x−h)2+k y = a(x - h)^2 + k \newlineHere, h=0 h = 0 and k=0 k = 0 , so the equation simplifies to y=ax2 y = ax^2 .
  2. Substitute Point for a: Substitute the point (88, −8-8) into the equation to find a a .\newlineUsing y=ax2 y = ax^2 , substitute x=8 x = 8 and y=−8 y = -8 .\newline−8=a(8)2-8 = a(8)^2\newline−8=64a-8 = 64a\newlinea=−864=−18 a = \frac{-8}{64} = -\frac{1}{8}
  3. Write Final Equation: Write the final equation using the value of a a .\newlineSubstitute a=−18 a = -\frac{1}{8} back into the simplified vertex form.\newliney=−18x2 y = -\frac{1}{8}x^2 \newlineThis is the equation of the parabola in vertex form.

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