equation in
vertex formπ = ππ^π + 4 find the Coordinates of
vertex
To find the vertex of an equation in vertex form, we simply need to look at the values of h and k.
π = π(π - π)^2 + π
In this equation, π represents the x-coordinate of the vertex, and π represents the y-coordinate of the vertex.
Comparing this to the equation given:
π = ππ^π + 4
We can see that π = 0 (since there is no x-term in the equation), and π = 4.
Therefore, the coordinates of the vertex are:
(π, π) = (0, 4)
To find the coordinates of the vertex, we can use the formula -b/2a. However, the equation you provided, y = 3x^2 + 4, is not in vertex form. The vertex form of a quadratic equation is y = a(x - h)^2 + k, where (h, k) represents the coordinates of the vertex.
To convert the equation y = 3x^2 + 4 into vertex form, we need to complete the square. Here are the steps:
1. Begin with the equation: y = 3x^2 + 4.
2. Factor out the common factor of 3 from the terms that involve x: y = 3(x^2 + 4/3).
3. To complete the square, take half of the coefficient of x (which is 0 in this case) and square it. Add this result inside the parentheses, but also subtract it outside the parentheses.
y = 3(x^2 + 0x + (0/2)^2 - (0/2)^2) + 4
y = 3(x^2 + 0x + 0) + 4
y = 3(x^2) + 4
4. Rewrite the equation, factoring the perfect square trinomial inside the parentheses.
y = 3(x^2) + 4
y = 3(x - 0)^2 + 4
5. Now we have the equation in vertex form: y = 3(x - 0)^2 + 4.
The coordinates of the vertex are (h, k) = (0, 4).
Therefore, the coordinates of the vertex for the equation y = 3x^2 + 4 are (0, 4).