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A parabola opening up or down has vertex (0,1)(0,1) and passes through (8,−15)(8,-15). Write its equation in vertex form.\newlineSimplify any fractions.

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Q. A parabola opening up or down has vertex (0,1)(0,1) and passes through (8,−15)(8,-15). Write its equation in vertex form.\newlineSimplify any fractions.
  1. Vertex Form: What is the vertex form of the parabola?\newlineThe vertex form of a parabola is given by the equation y=a(x−h)2+ky = a(x - h)^2 + k, where (h,k)(h, k) is the vertex of the parabola.
  2. Vertex at (0,1)(0, 1): What is the equation of a parabola with a vertex at (0,1)(0, 1)?\newlineSubstitute 00 for hh and 11 for kk in the vertex form.\newliney=a(x−0)2+1y = a(x - 0)^2 + 1\newliney=ax2+1y = ax^2 + 1
  3. Find Value of aa: Use the point (8,−15)(8, -15) to find the value of aa. Replace the variables with (8,−15)(8, -15) in the equation. Substitute 88 for xx and −15-15 for yy. −15=a(8)2+1-15 = a(8)^2 + 1 −15=64a+1-15 = 64a + 1
  4. Solve for a: Solve for a.\newline−15=64a+1-15 = 64a + 1\newlineSubtract 11 from both sides.\newline−16=64a-16 = 64a\newlineDivide both sides by 6464.\newline−1664=a-\frac{16}{64} = a\newlineSimplify the fraction.\newline−14=a-\frac{1}{4} = a
  5. Equation with a=−14a = -\frac{1}{4}: What is the equation of the parabola if a=−14a = -\frac{1}{4}?\newlineSubstitute −14-\frac{1}{4} for aa in the equation.\newliney=(−14)x2+1y = (-\frac{1}{4})x^2 + 1\newlineVertex form of the parabola: y=−14x2+1y = -\frac{1}{4}x^2 + 1

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