101k views
4 votes
Write the vertex form equation: f(x) = a(x - h)^2 + k. Enter the value of a for the given points (0, 5) and (2, -7). Help asap.

User Fhahn
by
8.6k points

1 Answer

4 votes

Final answer:

To find the value of 'a' in the vertex form equation using the given points (0, 5) and (2, -7), we can solve a system of equations by substituting the x and y values into the equation. Rearrange the equation to solve for the value of 'a' using algebraic manipulations.

Step-by-step explanation:

The vertex form equation of a quadratic function is given by f(x) = a(x - h)^2 + k. To find the value of a using the given points (0, 5) and (2, -7), we first need to substitute the x and y values into the equation. For the point (0, 5), we have 5 = a(0 - h)^2 + k, which simplifies to 5 = ah^2 + k. For the point (2, -7), we have -7 = a(2 - h)^2 + k, which simplifies to -7 = a(4 - 4h + h^2) + k.

To solve this system of equations, we can use the method of substitution. Let's solve the first equation for k: k = 5 - ah^2. Now, substitute this expression for k in the second equation: -7 = a(4 - 4h + h^2) + 5 - ah^2. Simplify the equation to obtain: -7 = 4a - 4ah + ah^2 + 5 - ah^2. Combine like terms to get: -7 = 4a - 4ah + 5. Finally, rearrange the equation to solve for a: a = (-7 - 5 + 4ah) / (4h - 4).

User Hoogw
by
7.4k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories