The vertex of a quadratic function is an important point that represents the highest or lowest value of the function, depending on the direction of the parabola. To find the vertex of the quadratic equation in the standard form, we can use the equation: y = ax^2 + bx + c.
In your case, the equation given seems to be y = 5x^2 + 0x + 3 (assuming it is a typographical error and you meant + 3 instead of + 42). Here, a = 5, b = 0, and c = 3.
The x-coordinate of the vertex can be calculated using the formula: x = - rac{b}{2a}.
- In this equation, we substitute the values of a and b:
- x = - rac{0}{2 imes 5} = 0.
Now that we have the x-coordinate, we can find the y-coordinate by substituting x = 0 back into the original equation:
- y = 5(0)^2 + 3 = 3.
Therefore, the vertex of the graph of the equation y = 5x^2 + 3 is at the point (0, 3).
In conclusion, the vertex of the graph of the quadratic equation is a critical point that can help understand the behavior of the function, indicating the minimum point in this case. If you would like to plot this graph, start at the vertex (0, 3), and note that the parabola opens upwards since the coefficient of x^2 is positive.