Question

Write the equation in Vertex form for the function

Answer 1

To write the equation in Vertex form for the function, we start with the standard form of a quadratic equation:

y = ax^2 + bx + c

Where y is the output variable, x is the input variable, and a, b, and c are constants.

To convert it to Vertex form, we complete the square for the x terms. The vertex form of a quadratic equation is:

y = a(x - h)^2 + k

Where (h, k) is the vertex of the parabola.

To find the vertex form of the equation, we need to rewrite the equation by completing the square for the x terms.

Given equation: y = 2x^2 + 8x - 3

First, factor out the common factor of 2 from the x^2 and x terms:

y = 2(x^2 + 4x) - 3

To complete the square, we take half of the coefficient of x and square it, then add and subtract that value inside the parentheses:

y = 2(x^2 + 4x + 4 - 4) - 3
y = 2((x + 2)^2 - 4) - 3
y = 2(x + 2)^2 - 8 - 3
y = 2(x + 2)^2 - 11

So, the equation in Vertex form is y = 2(x + 2)^2 - 11.