A parabola has the equation

y = 4(x-3)^2-7
Choose 2 true statements:
A) The parabola has a minimum value
B) The parabola has a maximum value
C) The parabola does not cross the y-axis
D) The parabola does not cross the x-axis
E) The vertex of the parabola is at the point with coordinates (-3,7)
F) The vertex of the parabola is at the point with coordinates (3,-7)

Can anyone help please?

For Further Reading

math - bobpursley, Monday, May 14, 2007 at 2:00pm
And your thinking is? You can graph this on your graphing calc, however, it can be answered by inspection.

Is it A & F??

You are correct! It is A & F. :)

To determine the true statements about the given parabola equation, we can analyze the equation and its properties.

The equation of the parabola is y = 4(x-3)^2-7.

A) The parabola has a minimum value: True. The coefficient of the squared term (4) is positive, indicating that the parabola opens upward. In this case, the parabola opens upward, which means it has a minimum value.

B) The parabola has a maximum value: False. The parabola opens upward, eliminating the possibility of having a maximum value.

C) The parabola does not cross the y-axis: False. By substituting x=0 into the equation, we find y = 4(0 - 3)^2 - 7 = 4(9) - 7 = 36 - 7 = 29. Since y is not equal to zero, the parabola does cross the y-axis.

D) The parabola does not cross the x-axis: True. Since the coefficient of the squared term (4) is positive, the parabola does not intersect the x-axis.

E) The vertex of the parabola is at the point with coordinates (-3,7): False. The x-coordinate of the vertex can be found by setting the equation equal to zero: 0 = 4(x - 3)^2 - 7. Solving for x, we get x - 3 = ±√(7/4). This gives us two potential x-coordinates for the vertex: x = 3 + √(7/4) and x = 3 - √(7/4). However, neither of these values is equal to -3, so the vertex is not at (-3,7).

F) The vertex of the parabola is at the point with coordinates (3,-7): True. By comparing the given equation to the vertex form of a parabola, y = a(x - h)^2 + k, we can identify that the vertex of the parabola is at the point (h, k). In this case, h = 3 (the x-coordinate of the vertex) and k = -7 (the y-coordinate of the vertex).

Therefore, the two true statements are:

A) The parabola has a minimum value.
F) The vertex of the parabola is at the point with coordinates (3,-7).

Yes, you are correct! The two true statements are:

A) The parabola has a minimum value.
F) The vertex of the parabola is at the point with coordinates (3,-7).

The parabola opens upward since the coefficient of x^2 is positive. This means it has a minimum value. The vertex of the parabola is given by (h, k), where h is the x-coordinate and k is the y-coordinate. In this case, the vertex is at (3,-7) which confirms statement F. Hope this helps!