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A parabola opening up or down has vertex (0,0)(0,0) and passes through (8,16)(8,16). Write its equation in vertex form.\newlineSimplify any fractions.\newline______

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Q. A parabola opening up or down has vertex (0,0)(0,0) and passes through (8,16)(8,16). Write its equation in vertex form.\newlineSimplify any fractions.\newline______
  1. Vertex Form of Parabola: Vertex form of parabola: y=a(x−h)2+ky = a(x - h)^2 + k Substitute 00 for hh and 00 for kk. y=a(x−0)2+0y = a(x - 0)^2 + 0 y=ax2y = ax^2
  2. Substitute and Simplify: Replace the variables with (8,16)(8, 16) in the equation. Substitute 88 for xx and 1616 for yy. 16=a(8)216 = a(8)^2 16=64a16 = 64a
  3. Solve for a: Solve for aa. 16=64a16 = 64a a=1664a = \frac{16}{64} a=14a = \frac{1}{4}
  4. Write Parabola Equation: Write the equation of the parabola. Substitute 14 \frac{1}{4} for a a . y=(14)x2 y = \left( \frac{1}{4} \right) x^2

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