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Zielflug [23.3K]
2 years ago
15

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

Mathematics
2 answers:
morpeh [17]2 years ago
4 0

Answer:

<u>B</u>

Step-by-step 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 : <u>x = -4</u>

<u />

=============================================================

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 <u>(-4, 0</u>)

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

weqwewe [10]2 years ago
3 0

Answer:

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

Step-by-step explanation:

Given table:

\large\begin{array}{| c | c | c | c | c | c | 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 <u>symmetry</u>.  

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

Therefore, the <u>line of symmetry</u> 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 <u>maximum</u>.

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

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