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VMariaS [17]
3 years ago
13

Find a quadratic function in standard form for each set of points

Mathematics
1 answer:
otez555 [7]3 years ago
5 0
For 1 the equation of the parabola is y = x^2 - 8x + 3
For 2 the equation of the parabola is y = -2x^2 - 3x + 1
For 3 the equation of the parabola is y = -x^2 + 5x - 4
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How do I draw and determine the equation of a trend line on a scatterplot
Nat2105 [25]

Step-by-step explanation:

Step 1: Draw your trend line.

You begin by drawing your trend line. You want your trend line to follow your data. You want to have roughly half your data above the line and the other half below the line, like this:

trend line equation

Step 2: Locate two points on the line.

Your next step is to locate two points on the trend line. Look carefully at your trend line and look for two easy to figure out points on the line. Ideally, these are points where the trend line crosses a clearly identifiable location.

For the trend line that we just drew, we can see these two easily identifiable points.

trend line equation

We can easily identify these two points as (3, 3) and (12, 6).

Step 3: Plug these two points into the formula for slope.

The formula for slope is this one:

trend line equation

We can label our first point as (x1,y1), and our second point as (x2,y2). So our x1 is 3, our y1 is 3, our x2 is 12, and our y2 is 6. Plugging these values into the equation for slope and evaluating, we get this:

trend line equation

So our slope is 1/3.

8 0
3 years ago
Given the midpoint and one endpoint of a line segment, find the other endpoint.
lozanna [386]

\bf ~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ (\stackrel{x_1}{\frac{5}{8}}~,~\stackrel{y_1}{\frac{27}{8}})\qquad  (\stackrel{x_2}{x}~,~\stackrel{y_2}{y}) \qquad \left(\cfrac{ x_2 +  x_1}{2}~~~ ,~~~ \cfrac{ y_2 +  y_1}{2} \right) \\\\\\ \left( \cfrac{x+\frac{5}{8}}{2}~~,~~\cfrac{y+\frac{27}{8}}{2} \right)=\stackrel{midpoint}{\left( -\frac{7}{6}~~,~~-\frac{10}{3} \right)}

\bf -------------------------------\\\\ \cfrac{x+\frac{5}{8}}{2}=-\cfrac{7}{6}\implies  x+\cfrac{5}{8}=-\cfrac{14}{6}\implies x=-\cfrac{14}{6}-\cfrac{5}{8} \\\\\\ x=\cfrac{-14(4)-5(3)}{24}\implies x=\cfrac{-56-15}{24}\implies \boxed{x=-\cfrac{71}{24}}\\\\ -------------------------------\\\\ \cfrac{y+\frac{27}{8}}{2}=-\cfrac{10}{3}\implies y+\cfrac{27}{8}=-\cfrac{20}{3}\implies y=-\cfrac{20}{3}-\cfrac{27}{8} \\\\\\ y=\cfrac{-20(8)-27(3)}{24}\implies y=\cfrac{-160-81}{24}\implies \boxed{y=-\cfrac{241}{24}}

3 0
3 years ago
Use synthetic division to find the result when 3x^3 + 13x^2 + x – 12 is divided by<br> X + 4.
IgorC [24]

Answer:

3x² + x - 3

Step-by-step explanation:

The way I like to do it is to get rid of the x's and just use the numbers in the case of synthetic division

Pretend the square root of the division symbol

-4 √ 3 12 1 -12

Quick note: We're dividing by -4 because we're dividing by x + 4

First bring down the 3

-4 √ 3 13 1 -12

      3

Multiply it by 4 then bring add it to the next number

-4 √ 3 13 1 -12

          -12

       3   1

Add that number to the next one

-4 √ 3 13 1 -12

        -12 -4

      3    1   -3

Finally repeat the step for the last number

-4 √ 3 13 1 -12

       3 -12 -4 +12

       3    1   -3   0

Now take those bottom numbers and add back the x's but with one less power, so the starting x³ would now become x², x² would become x, and so on

3x² + 1x - 3

8 0
2 years ago
Leslie found the volume of a cone having both a height
Mademuasel [1]

Answer:

D.No, she forgot to take one-third of the base area times height.

Step-by-step explanation:

I just did it and its right.

6 0
3 years ago
Read 2 more answers
What’s the slope of the line?
yulyashka [42]

Answer:

the slope is 1

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
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