Given the next quadratic function:
![y=2x^2+3x-2](https://tex.z-dn.net/?f=y%3D2x%5E2%2B3x-2)
to sketch its graph, first, we need to find its vertex. The x-coordinate of the vertex is found as follows:
![x_V=\frac{-b}{2a}](https://tex.z-dn.net/?f=x_V%3D%5Cfrac%7B-b%7D%7B2a%7D)
where <em>a</em> and <em>b</em> are the first two coefficients of the quadratic function. Substituting with a = 2 and b = 3, we get:
![\begin{gathered} x_V=\frac{-3}{2\cdot2} \\ x_V=-\frac{3}{4}=-0.75 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20x_V%3D%5Cfrac%7B-3%7D%7B2%5Ccdot2%7D%20%5C%5C%20x_V%3D-%5Cfrac%7B3%7D%7B4%7D%3D-0.75%20%5Cend%7Bgathered%7D)
The y-coordinate of the vertex is found by substituting the x-coordinate in the quadratic function, as follows:
![\begin{gathered} y_V=2x^2_V+3x_V-2 \\ y_V=2\cdot(-\frac{3}{4})^2+3\cdot(-\frac{3}{4})-2 \\ y_V=2\cdot\frac{9}{16}+3\cdot(-\frac{3}{4})-2 \\ y_V=\frac{9}{8}-\frac{9}{4}-2 \\ y_V=-\frac{25}{8}=-3.125 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20y_V%3D2x%5E2_V%2B3x_V-2%20%5C%5C%20y_V%3D2%5Ccdot%28-%5Cfrac%7B3%7D%7B4%7D%29%5E2%2B3%5Ccdot%28-%5Cfrac%7B3%7D%7B4%7D%29-2%20%5C%5C%20y_V%3D2%5Ccdot%5Cfrac%7B9%7D%7B16%7D%2B3%5Ccdot%28-%5Cfrac%7B3%7D%7B4%7D%29-2%20%5C%5C%20y_V%3D%5Cfrac%7B9%7D%7B8%7D-%5Cfrac%7B9%7D%7B4%7D-2%20%5C%5C%20y_V%3D-%5Cfrac%7B25%7D%7B8%7D%3D-3.125%20%5Cend%7Bgathered%7D)
The factorization indicates that the curve crosses the x-axis at the points (-2, 0) and (1/2, 0). We also know that the curve crosses the y-axis at (0,-2). Connecting these points and the vertex (-0.75, -3.125) with a U-shaped curve, we get:
Answer:
<h2>
1240.4 mm²</h2>
Step-by-step explanation:
![440.4 + 5\cdot(\frac12\cdot16\cdot20)=440.4+800=1240.4\ mm^2](https://tex.z-dn.net/?f=440.4%20%2B%205%5Ccdot%28%5Cfrac12%5Ccdot16%5Ccdot20%29%3D440.4%2B800%3D1240.4%5C%20mm%5E2)
Simple...
you have:
1.) Find the slope of the line using (-2,1) and (3,6)
Using
![\frac{ y_{1}- y_{2} }{ x_{1} - x_{2} }](https://tex.z-dn.net/?f=%20%5Cfrac%7B%20y_%7B1%7D-%20%20y_%7B2%7D%20%7D%7B%20x_%7B1%7D%20-%20x_%7B2%7D%20%20%7D%20)
![\frac{1-6}{-2-3} = \frac{-5}{-5}](https://tex.z-dn.net/?f=%20%5Cfrac%7B1-6%7D%7B-2-3%7D%20%3D%20%5Cfrac%7B-5%7D%7B-5%7D%20)
m=1 (slope)
2.)Tell whether the equation, 8y+3=5x+3, is a direct variation.
y=
![\frac{5x}{8}](https://tex.z-dn.net/?f=%20%5Cfrac%7B5x%7D%7B8%7D%20)
(None)
3.)What is the slope and y-intercept of the graph of the equation y=2x+3?
Slope =2
y-intercept=3
C.
Thus, your answer.
Answer:
Slope=2.
Step-by-step explanation:
Slope=y1-y2/x1-x2
Where
X1,y1,=(-5, -11) X2,y2=(6,11).
Slope=-11-11/-5-6
=-22/-11
=22/11
=2
Slope is 2
You have to divide 1.25 by .25 the answer is 5 servings