Find the equation of the axis of symmetry and the coordinates of the vertex of the graph of the function y = 4x2 + 5x – 1.
1 answer:
Graph the parabola using the direction, vertex, focus, and axis of symmetry.
Direction: Opens Up
Vertex: <span>(−<span>5/8</span>,−<span>41/16</span>)</span>
Focus: <span>(−<span>5/8</span>,−<span>5/2</span>)</span>
Axis of Symmetry: <span>x=−<span>5/8</span></span>
Directrix: <span>y=−<span>21/8</span></span><span><span> x. y
</span><span><span>−3. </span>20
</span><span><span>−2. </span>5
</span><span><span>−<span>5/8. </span></span><span>−<span>41/16
</span></span></span><span> 0. <span>−1
</span></span><span>1. <span>8
</span></span></span>
Direction: Opens Up
Vertex: <span>(−<span>5/8</span>,−<span>41/16</span>)</span>
Focus: <span>(−<span>5/8</span>,−<span>5/2</span>)</span>
Axis of Symmetry: <span>x=−<span>5/8</span></span>
Directrix: <span>y=−<span>21/8</span></span><span><span> x. y
</span><span><span>−3. </span>20
</span><span><span>−2. </span>5
</span><span><span>−<span>5/8. </span></span><span>−<span>41/16
</span></span></span><span> 0. <span>−1
</span></span><span>1. <span>8
</span></span></span>
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Answer:
The 95% confidence interval obtained with a sample size of 64 will give greater precision.
Step-by-step explanation:
We are given the following in the question:
A 95% confidence interval is calculated with the following sample sizes
The population mean and standard deviation are unknown.
Effect of sample size on confidence interval:
- As the sample size increases the margin of error decreases.
- As the margin of error decreases the width of the confidence level decreases.
- Thus, with increased sample size the width of confidence level decreases.
If we want a confidence interval with greater precision that is smaller width, we have to choose the higher sample size.
Thus, the 95% confidence interval obtained with a sample size of 64 will give greater precision.