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2 years ago

Find the slope or rate of change.

Mathematics

1 answer:

Dima020 [189]2 years ago

3 0

Answer:

$m=\frac{5}{3}$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Algebra I

Slope Formula: $m=\frac{y_2-y_1}{x_2-x_1}$

Step-by-step explanation:

Step 1: Define

Find points from graph

Point (-2, 0)

Point (1, 5)

Step 2: Find slope m

Substitute: $m=\frac{5-0}{1+2}$
Subtract/Add: $m=\frac{5}{3}$

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Hope it helps.

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3 years ago

Which second-degree polynomial function has a leading coefficient of –1 and root 5 with multiplicity 2?

PIT_PIT [208]

A second degree polynomial function has the general form:

$\displaystyle{f(x)=ax^2+bx+c$ , where $a\neq0$ .

The leading coefficient is a, so we have a=-1.

5 is a double root means that :

i) f(5)=0,
ii) the discriminant D is 0, where $D=b^2-4ac$ .

Substituting x=5, we have

f(5)=a(5)^2+b(5)+c,

and since f(5)=0, and a is -1 we have:

0=-25+5b+c
thus c=25-5b.

By ii) $\displaystyle{b^2-4ac=0$ .

Substituting a with -1 and c with 25-5b we have:

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Finally we find c: c=25-5b=25-50=-25

Thus the function is       $\displaystyle{f(x)=-x^2+10x-25$

Remark: It is also possible to solve the problem by considering the form

$f(x)=-1(x-5)^2$ directly.

In general, if a quadratic function has leading coefficient a, and has a root r of multiplicity 2, then its form is $f(x)=a(x-r)^2$

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I also included an image showing the decimal place moved to the right.

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