Write Quadratic Function Given Vertex And Another Point Worksheet

Algebra 2
Quadratic Functions

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How Will This Worksheet on “Write Quadratic Function Given Vertex and Another Point” Benefit Your Student's Learning?

  • Learning to write quadratic functions from the vertex and another point deepens understanding of quadratic functions and their properties.
  • It fosters critical thinking as students analyze the details related to the vertex.
  • Improves skills in solving algebra problems by applying theoretical knowledge.
  • Enhances problem-solving abilities and mathematical literacy.
  • Prepares students for advanced mathematical concepts and real-world applications.

How to Write Quadratic Function Given Vertex and Another Point?

  • Determine the values of \(h\) and \(k\) from the vertex coordinates of the parabola.
  • Substitute the values of \(h\) and \(k\) into the vertex form of the parabola: \( f(x) = a(x - h)^2 + k \).
  • Find the value of \(a\) by substituting the \(x\) and \(y\) coordinates from the given additional point.
  • Write the quadratic function by substituting the calculated value of \(a\) back into the vertex form.

Solved Example

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______
Solution:
  1. Vertex Form of Parabola: Vertex form of parabola: y=a(xh)2+ky = a(x - h)^2 + k Substitute 00 for hh and 00 for kk. y=a(x0)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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About Worksheet

Algebra 2
Quadratic Functions

Writing a quadratic function from its vertex and an additional point involves creating the equation of a parabola using the vertex \((h, k)\) and another known point. The vertex form is \( f(x) = a(x - h)^2 + k \). This process includes finding the vertex form and calculating the coefficient \(a\) using the extra point. In these worksheets, students will practice determining the vertex form and the value of \(a\) to write the quadratic function's equation.

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