Question

1. find the minimum or maximum of the following:

\\4x^2 + 16x - 15\\

a) minimum: 33
b) minimum: -31
c) maximum: 33
d) maximum: -31
e) none of the above

Explanation:

Find the axis of symmetry for Question 9

Using the Axis of Symmetry knowledge point

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Find the extremum for Question 11

Identify the direction and vertex of the parabola \(g(x) = 4x^2 + 16x - 15\).
Since the leading coefficient \(a = 4 > 0\), the parabola opens upward, meaning it has a minimum value at its vertex.
We find the \(x\)-coordinate of the vertex:

$$ x = -\frac{b}{2a} = -\frac{16}{2(4)} = -2 $$

Now, evaluate the function at \(x = -2\) to find the minimum value:

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$$

Thus, the minimum value is \(-31\).

Identify the vertex and graph for Question 13

Using the Parabola Vertex Form knowledge point

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Looking at the options:

• Graph (a) has its vertex in the fourth quadrant at \((3, -1)\).
• Graph (b) has its vertex in the fourth quadrant but shifted further right or down, specifically at \((4, -3)\) or similar. Let's inspect the grid:
• In graph (a), the vertex is located at \(x = 3\), \(y = -1\).
• In graph (b), the vertex is located at \(x = 5\), \(y = -2\).

Therefore, graph (a) represents the function \(f(x) = 2(x - 3)^2 - 1\).

Answer:

No.	Answer
11	(b) Minimum: -31
13	(a)