Question

The table represents quadratic function g. Which statement is true about the function?

I
-5
-4 -3
-2 -1 0
-1
0
-1
-4 -9 -16
O A. The minimum occurs at the function's x-intercept.
O B.
The maximum occurs at the function's x-intercept.
O C.
The maximum occurs at the function's y-intercept.
The minimum occurs at the function's y-intercept.
O D.

Answer 1

B

Explanation:

Finding the line of symmetry :

⇒ Two x-values have the same y-coordinate → (-5) and (-3)

⇒ This means the symmetry is exhibited and it lies between these 2 x-values

⇒ Line of symmetry : x = -4

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Now, on plotting these points on a graph we see that this graph has a negative coefficient.

⇒ This means this graph will have a maximum point as the vertex

⇒ The vertex lies on the line of symmetry, hence the vertex (according to the graph and table) is (-4, 0)

Hence, we can say that the maximum occurs at the function's x-intercept.

Answer 2

B. The maximum occurs at the function's x-intercept.

Explanation:

Given table:

`\large\begin{array} c \cline{1-7} x & -5 & -4 & -3 & -2 & -1 & 0\\\cline{1-7} g(x) & -1 & 0 & -1 & -4 & -9 & -16\\\cline{1-7}\end{array}`

From inspection of the table, we can see that:

• 
  `g(-5) = -1` and
• 
  `g(-3) = -1`

This indicates symmetry.

The line of symmetry is the mid-point between the two x-values.

Therefore, the line of symmetry is x = -4

The vertex (minima/maxima) is on the line of symmetry, therefore the vertex is at (-4, 0). As the function decreases as x → 0, the vertex is a maximum.

As the y-value of the vertex is 0, the maximum occurs at the function's x-intercept.