Question

Which of the following equations is of a parabola with a vertex at (0,-5)?

a. y=(x - 5)^2
b. y= (x + 5)^2
c. y=x^2-5
d. y= x^2 +5

Answer 1

The equation of a parabola with a vertex at (0,-5) is c. y = x^2 - 5, as it follows the general form of a parabola's equation.

Step-by-step explanation:

The equation of a parabola with a vertex at a specific point can be determined by analyzing the general form of a parabola's equation, which is y = a(x - h)^2 + k, where (h,k) is the vertex of the parabola. Looking at the options provided:

• y = (x - 5)^2 has its vertex at (5,0).
• y = (x + 5)^2 would have the vertex at (-5,0).
• y = x^2 - 5 is in the form y = a(x - 0)^2 - 5, which indicates that the vertex is at (0,-5).
• y = x^2 + 5 also has the vertex at (0,5).

Thus, the correct equation representing a parabola with a vertex at (0,-5) is c. y = x^2 - 5.