All categories

3 years ago

Graph y greater than or equal to (x+2)^2

Mathematics

1 answer:

katovenus [111]3 years ago

3 0

Answer:

See attached image

Step-by-step explanation:

The graph of $y\geq (x+2)^2$ is not the one shown on the picture. Although the highlighted are (above the curve) is correct, since that corresponds to the y-values larger than those of the parabola, the problem is that in the picture given, the actual trace of the parabola (which corresponds to the equality $y=(x+2)^2$ , is shown with dotted trace - which by convention indicates that the trace is NOT included.

Since the inequality symbol in our inequality DOES contain the equal sign (larger than OR EQUAL to), the parabola's trace should be represented with a solid line. (see attached image)

You might be interested in

Write the given roots to quadraatic equation

german

Answer:

It's like solving a quadratic, but in reverse, and in this case you'll arrive at x2+x−12=0

Explanation:

We're going to go "backwards" with this problem - normally we're asked to take a quadratic equation and find the roots. So we'll do what we normally do, but in reverse:

Let's start with the roots:

x=3, x=−4

So let's move the constants over with the x terms to have equations equal to 0:

x−3=0, x+4=0

Now we can set up the equation, as:

(x−3)(x+4)=0

We can now distribute out the 2 quantities:

x2+x−12=0

6 0

3 years ago

Write the Slope-Intercept and Point-Slope forms of the line passing through the point (-3, 2) and having a slope of -4/5

weeeeeb [17]

Answer:

slope-intercept: $y=\frac{-4}{5} x-\frac{2}{5}$

point-slope: $y-2=\frac{-4}{5} (x+3)$

Step-by-step explanation:

The slope-intercept form of a line is written as y = mx + b, where m is the slope and b is the y-intercept.

The point-slope form of a line is written as y - y1 = m(x - x1), where (x1, y1) is a given point and m is the slope.

Here, we see that the slope is -4/5, which means that m = -4/5. Since we're given a point (-3, 2), let's go ahead and just write the point-slope form already. (x1, y1) = (-3, 2) so x1 = -3 and y1 = 2. Then:

y - y1 = m(x - x1)

y - 2 = (-4/5) * (x + 3)

$y-2=\frac{-4}{5} (x+3)$

Now, we want to find the slope-intercept form, so we need to figure out the y-intercept. Well, first, let's plug in what we know:

y = mx + b

y = (-4/5)x + b

Any point on this line will satisfy the above equation. Since (-3, 2) is on this line, if we plug -3 in for x and 2 in for y, the equation should hold true, so we can solve for b:

y = (-4/5)x + b

2 = (-4/5) * (-3) + b

2 = 12/5 + b

b = -2/5

So, the y-intercept is -2/5. Then the slope-intercept form is:

$y=\frac{-4}{5} x-\frac{2}{5}$

Thus, our two equations are:

slope-intercept: $y=\frac{-4}{5} x-\frac{2}{5}$

point-slope: $y-2=\frac{-4}{5} (x+3)$

8 0

3 years ago

Using the formula for initial velocity h=-16t2+VT the height of any object can be found by the time, Annalee serves a volleyball