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Leviafan [203]
3 years ago
11

Describe the graph of the function. y = |x – 4| – 7

Mathematics
1 answer:
Lemur [1.5K]3 years ago
5 0

Answer:

This is always ''interesting'' If you see an absolute value, you always need to deal with when it is zero:

(x-4)=0 ===> x=4,

so that now you have to plot 2 functions!

For x<= 4: what's inside the absolute value (x-4) is negative, right?, then let's make it +, by multiplying by -1:

|x-4| = -(x-4)=4-x

Then:

for x<=4, y = -x+4-7 = -x-3

for x=>4, (x-4) is positive, so no changes:

y= x-4-7 = x-11,

Now plot both lines. Pick up some x that are 4 or less, for y = -x-3, and some points that are 4 or greater, for y=x-11

In fact, only two points are necessary to draw a line, right? So if you want to go full speed, choose:

x=4 and x= 3 for y=-x-3

And just x=5 for y=x-11

The reason is that the absolute value is continuous, so x=4 works for both:

x=4===> y=-4-3 = -7

x==4 ====> y = 4-11=-7!

abs() usually have a cusp int he point where it is =0

Step-by-step explanation:

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The discriminant of the given quadratic equation as in the task content can be evaluated by means of the formula; D = b²-4ac and it's value is; 13.

<h3>What is the discriminant of the quadratic equation as given in the task content?</h3>

According to the task content, it follows that the quadratic equation whose discriminant is to be determined is; x²-5x+3=0.

By comparison with the standard form equation of a quadratic graph which goes thus; ax²+bx +c = 0, in which case, the determinant is given by the expression; b² - 4ac.

We can consequently evaluate the determinant of the quadratic equation in discuss as follows;

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Hence, the determinant in this case is; 13.

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