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?
And your thinking is? You can graph this on your graphing calc, however, it can be answered by inspection.
poop in the toilet
To determine which statements are true for the given parabola equation, we can analyze its form and key characteristics.
First, let's look at the general form of the equation for a parabola: y = a(x-h)^2 + k, where (h, k) represents the vertex of the parabola.
Comparing this with the given equation y = 4(x-3)^2 - 7, we can observe that the vertex of the parabola is at (3, -7). Therefore, option F) "The vertex of the parabola is at the point with coordinates (3,-7)" is true.
Now, let's discuss each statement and analyze its validity:
A) The parabola has a minimum value: This is true since the coefficient "a" in the equation is positive (4 > 0). When "a" is positive, it indicates that the parabola opens upward, and hence, it has a minimum value. Therefore, option A) "The parabola has a minimum value" is true.
B) The parabola has a maximum value: This is false because the parabola opens upward, as indicated by the positive coefficient "a". Only downward-opening parabolas have a maximum value.
C) The parabola does not cross the y-axis: This is false. The parabola intersects the y-axis when x = 0. By substituting x = 0 into the equation y = 4(x-3)^2 - 7, we find y = 4(0-3)^2 - 7 = 4(9) - 7 = 36 - 7 = 29. Therefore, the parabola does cross the y-axis.
D) The parabola does not cross the x-axis: This is true. Since the vertex of the parabola is located above the x-axis (at (3, -7)) and the parabola opens upward, it will not intersect the x-axis. Therefore, option D) "The parabola does not cross the x-axis" is true.
Hence, the true statements are A) "The parabola has a minimum value" and D) "The parabola does not cross the x-axis".