Q. A parabola opening up or down has vertex (0,5) and passes through (6,−4). Write its equation in vertex form.Simplify any fractions.
Vertex Form Explanation: What is the vertex form of the parabola?The vertex form of a parabola is given by the equation y=a(x−h)2+k, where (h,k) is the vertex of the parabola.
Equation with Vertex: What is the equation of a parabola with a vertex at (0,5)?Substitute 0 for h and 5 for k in the vertex form.y=a(x−0)2+5y=ax2+5
Use Point to Find 'a': Use the point (6,−4) to find the value of 'a'.Replace the variables with (6,−4) in the equation.Substitute 6 for x and −4 for y.−4=a(6)2+5−4=36a+5
Solve for 'a': Solve for 'a'.−4=36a+5Subtract 5 from both sides.−4−5=36a−9=36aDivide both sides by 36.−369=aSimplify the fraction.−41=a
Write Equation with 'a': Write the equation of the parabola using the value of 'a'.Substitute −41 for a in the equation y=ax2+5.y=(−41)x2+5Vertex form of the parabola: y=−(41)x2+5
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