# Write Quadratic Function Given Vertex And Another Point Worksheet

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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.

Algebra 2

## 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 $(0,0)$ and passes through $(8,16)$. Write its equation in vertex form.$\newline$Simplify any fractions.$\newline$______
Solution:
1. Vertex Form of Parabola: Vertex form of parabola: $y = a(x - h)^2 + k$ Substitute $0$ for $h$ and $0$ for $k$. $y = a(x - 0)^2 + 0$ $y = ax^2$
2. Substitute and Simplify: Replace the variables with $(8, 16)$ in the equation. Substitute $8$ for $x$ and $16$ for $y$. $16 = a(8)^2$ $16 = 64a$
3. Solve for a: Solve for $a$. $16 = 64a$ $a = \frac{16}{64}$ $a = \frac{1}{4}$
4. Write Parabola Equation: Write the equation of the parabola. Substitute $\frac{1}{4}$ for $a$. $y = \left( \frac{1}{4} \right) x^2$

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