Answer the questions about the key characteristics of the function below

Question

(1.5,4)
( 0.5,0) (2.5,0)
(0, z5)

Anis of symmetry blank
Does this fuction have a minimum or maximum? Blank
X-intercepts blank
Y- intercepts

Minimum
Maximum
x = 1.5
y = 4
(0,5)
(0.5,0) and ( 2.5,0)
(-5,0)
(0.0.5) and (0,2.5)

Answer 1

To answer your questions regarding the key characteristics of the function described by the points (1.5, 4), (0.5, 0), (2.5, 0), and (0, z5) (presumably (0, 5)), we first need to clarify certain aspects of the function based on those points.

1. Axis of Symmetry: The axis of symmetry for a quadratic function in standard form is found using the formula $x=-\frac{b}{2a}$. If these points represent a parabola (which appears likely due to the minimum/maximum consideration), you would find the axis of symmetry halfway between the x-intercepts, which here are at (0.5, 0) and (2.5, 0). The midpoint is: $$x=\frac{0.5+2.5}{2}=\frac{3}{2}=1.5$$ So, the axis of symmetry is x = 1.5.

2. Does this function have a minimum or maximum? Since the vertex (1.5, 4) represents a peak point between the endpoints defined by the x-intercepts (0.5, 0) and (2.5, 0), this indicates that the parabola opens downward. Thus, it has a maximum at this vertex.

3. X-intercepts: The x-intercepts of the function are the points where the function crosses the x-axis. From the provided points, the x-intercepts are:

   • (0.5, 0)
   • (2.5, 0)

   So, the x-intercepts are (0.5, 0) and (2.5, 0).

4. Y-intercept: The y-intercept is where the function crosses the y-axis, which is found at the point where $x=0$. The value at (0, 5) indicates that the y-intercept is (0, 5).

To summarize:

• Axis of Symmetry: x = 1.5
• Has a minimum or maximum: Maximum
• X-intercepts: (0.5, 0) and (2.5, 0)
• Y-intercept: (0, 5)

So, final answers in the indicated blanks format:

Axis of symmetry: x = 1.5
Does this function have a minimum or maximum? Maximum
X-intercepts: (0.5, 0) and (2.5, 0)
Y-intercept: (0, 5)