Opens up or down?
The equation in vertex for y=3x^2+4
The parabola represented by the equation y=3x^2+4 opens up because the coefficient of x^2 is positive.
To find the vertex of the parabola, we can use the formula x = -b/2a, where a is the coefficient of x^2 and b is the coefficient of x.
In this case, a = 3 and b = 0 (since there is no x term). So x = -0/(2*3) = 0.
To find the corresponding y-coordinate of the vertex, we can plug in x = 0 to the equation:
y = 3(0)^2 + 4 = 4
Therefore, the vertex of the parabola y=3x^2+4 is (0, 4).
To determine whether the graph of the equation y=3x^2+4 opens up or down, we can look at the coefficient of the x^2 term.
In this equation, the coefficient of the x^2 term is positive (+3). When the coefficient of the x^2 term is positive, the graph of the equation opens upward.
Therefore, the equation y=3x^2+4 opens up.