What are the coordinates of the vertex of the quadratic function y = x squared + 7?

To identify the coordinates of the vertex of the quadratic function given by the equation ( y = x^2 + 7 ), it's important to recognize the standard form of a quadratic function, which is typically expressed as ( y = ax^2 + bx + c ). In this case, the function can be rewritten as ( y = 1x^2 + 0x + 7 ).

The vertex of a parabola described by such an equation occurs at the point where the value of ( x ) is zero (since there is no linear ( bx ) term to shift it left or right). The function ( x^2 ) achieves its minimum value of 0 when ( x = 0 ).

Substituting ( x = 0 ) into the equation yields:

[

y = (0)^2 + 7 = 0 + 7 = 7

]

Thus, the vertex of the quadratic function, which is the minimum point in this case, is at the coordinates ( (0, 7) ). This confirms that ( (0, 7) ) is indeed the vertex of the function.

Understanding this principle can help differentiate the vertex from other points