the graph will open down
The graph will have a maximum value
The graph will be narrow
the graph can be moved right and left.
the graph can be moved up and down.
Step-by-step explanation:
The graph of F(x)= -4(x+3)²+2 is a parabola.
Plotting the graph:
a) It opens downward
Hence, the graph will open down
b) Its maximum value is at x = -3
The graph will have a maximum value.
c) To determine if the graph will be narrow or wide, we use the formula for the quadratic function:
ax² + bx + c = 0
If a > 0, it will be wide, if a < 0, it will be narrow. The closer the coefficient of x² is to zero, the wider it is.
Expanding -4(x+3)²+2 = -4(x²+6x + 9) +2 = -4x² - 24x - 36 + 2
we see above, the value of a which is the coefficient of x² is negative; less than 0
Note: without expanding, we can determine it. -4 outside the expression indicates it is less than zero.
Hence, the graph will be narrow
d) A graph of a function can be moved left or right. Adding to the input of the function moves the graph left, subtracting from the input of the function moves the graph right.
The input is the x value
Hence, the graph can be moved right and left.
e) A graph of a function can be moved up or down. Adding to the output of the function moves the graph up, subtracting from the output of the function moves the graph down.
The output is the y value
Hence, the graph can be moved up and down.