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

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

• A. (0, 0)
• B. (0, 7)
• C. (7, 0)
• D. (1, 1)

Answer: (B)

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

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