Identify the like terms.

When graphing y = 2x2 + 35x + 75, which viewing window would allow you to see all of the intercepts and the minimum as closely a

djverab [1.8K]

The intercept with the y-axes occurs when x = 0

f(0) = 2*02 + 35*0 + 75 = 0 + 0 + 75 = 75

So intercept with x axes is the point (0,75)

The intercept with the x-axes occurs when y=0

2x2 + 35x + 75 = 0

As there’s no direct way to find x, we can use the Bhaskara formula:

x=(-b+- square root (b2-4ac))/(2a)

This formula is for: ax2 +bx + c = 0

So:

a=2

b=35

c=75

x=(-35+- square root (35^2-4*2*75))/(2*2)

So x can be -2.5 or -15

So intercept with y axes are the points (-2.5,0) and (-15,0)

And there is also a formula to find the mínimum. The mínimum is always the vertex:

Xv = -b/(2*a) = -35/(2*2) = -8.75

Yv = f(Xv) = f(-8.75) = 2(-8.75)^2 + 35(-8.75) + 75 = -78.125

So the minimum is the point (-8.75, -78.125)

You can easily verify all these data with a graphic software such as GeoGebra.

Here is the complete list of all the points we need to see:

(0,75); (-2.5,0) ; (-15,0), (-8.75, -78.125)

So the mínimum X has to be -15 and the máximum X has to be 0

and the mínimum Y has to be -78.125 and the máximum Y has to be 75

So this leads to a different scale for X and for Y.

Window x = [ -15, 0] y = [ -78.125, 75]

5 0

2 years ago

Easy question, easy points

Juli2301 [7.4K]

Answer:

Step-by-step explanation:

The solution of a system of linear equations is the point of intersection of their graphs because the intersection represents the only x or y values that will satisfy both/all equations. The graph visually shows that the intersection of these equations is the only spot on the graph that all of the equations have in common. This means that only this spot will satisfy all equations. For example, the intersection may be (0,1); this means that for all equations an x value of 0 will always result in the y value of 1. However, an x or y value that satisfies one equation may not satisfy the others if they do not lead to the desired outcome.

3 0

3 years ago

10 points!!! Please answer 8 and 9 and hurry

lilavasa [31]

Answer:

Step-by-step explanation:

since EG bisects angle DEF

31 = x + 15

31 - 15 = x

x = 16 degree

6x - 4 = 56

6x = 56 + 4

x = 60/6

x = 10

4 0

3 years ago

Read 2 more answers

Which graph represents this system? 2 x minus 5 y = negative 5. y = two-fifths x + 1.

Softa [21]

Answer:

The answer is the first graph.

Step-by-step explanation:

I did it on edge. I got it wrong the first time because I used an answer from this question. Because of that, I reported it. Now I have the correct answer lol.

6 0

3 years ago

Read 2 more answers

The coordinates of rectangle ABCD are A(1, 2), B(4, 5),C(9, 0) and D(6, -3). What is the area of the rectangle? 18 square units

Natali5045456 [20]

In order to find the area of a rectangle, the formula is L*W (Length multiplied by Width). Our goal is to find these two measurements, so we will take the following steps:
1) Plot the coordinates on a graph (I have attached a visual guide)
2) Using the Pythagorean Theorem, or the Distance formula we can find the length and width: $\sqrt{(x_{2}-x_{1} )^{2} +(y_{2}-y_{1} )^{2}$
3) We will use these values in the Area formula for a rectangle (L*W)
4) After solving the Area formula with the values retrieved from the Distance Formula we find that the area is roughly 30 units squared.

4 0

3 years ago