Question

Rewrite equation in veryex form
y=1/3x^2 +4x+7

Answer 1

To rewrite the equation in vertex form, follow these steps: factor out the coefficient of x^2, complete the square, rearrange the terms, and simplify to obtain the equation in vertex form. The resulting equation is y = (1/3)(x + 6)^2 - 5.

Step-by-step explanation:

To rewrite the equation in vertex form, we can complete the square. The vertex form of a quadratic equation is y = a(x - h)^2 + k, where (h, k) is the vertex of the parabola. Let's go through the steps:

1. Start with the given equation: y = (1/3)x^2 + 4x + 7
2. Factor out the coefficient of x^2 (1/3): y = (1/3)(x^2 + 12x + 21)
3. To complete the square, take half of the coefficient of x (12/2 = 6) and square it (6^2 = 36).
4. Add and subtract the value obtained in step 3 inside the bracket: y = (1/3)(x^2 + 12x + 36 - 36 + 21)
5. Rearrange the terms: y = (1/3)(x^2 + 12x + 36 - 36 + 21)
6. A factor of (x + 6)^2 is obtained by taking the square root of the first three terms: y = (1/3)((x + 6)^2 - 15)
7. Simplify and rewrite the equation in vertex form: y = (1/3)(x + 6)^2 - 5