Equation in

Question

vertex form𝒚 = 𝟑𝒙𝟐 + 4 find the Coordinates of
vertex

Answer 1

To convert the equation 𝑦 = 3𝑥^2 + 4 into vertex form, we need to complete the square.

Firstly, we factor the coefficient of x^2 out of the equation, which gives us:

𝑦 = 3(x^2 + 4/3)

Next, we need to add and subtract a constant term to the parenthetical expression inside the parentheses. We can do this by taking half of the coefficient of x (which is 0 in this case) and squaring it.

(0/2)^2 = 0

So we add and subtract 0 inside the parentheses:

𝑦 = 3(x^2 + 4/3 + 0 - 0)

Now we can write this expression in vertex form by factoring the perfect square inside the parentheses and applying the distributive property:

𝑦 = 3((x + 0)^2 + 4/3 - 0)

Simplifying this expression gives us:

𝑦 = 3(x + 0)^2 + 4

Therefore, the vertex of this equation is (0,4).