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Kay [80]
2 years ago
6

Do you agree with the statement that " cubic functions must have at least 1 x-intercept but not more than 3, whereas quadratic f

unctions may or may not have x-intercepts
Mathematics
1 answer:
vladimir2022 [97]2 years ago
3 0

Answer:

Yes, I agree

Step-by-step explanation:

For the cubic function

A cubic function is represented as:

f(x)=ax^3+bx^2+cx+d

A cubic function may have 1, 2 or 3 x intercepts. This is shown below

For 3 x intercepts

y = x^3 - x

Equate y to 0

x^3 - x = 0

Expand

x(x^2 - 1) = 0

Express x^2 - 1 as difference of two squares

x(x - 1)(x +1 ) = 0

<em>x = 0 or 1 or -1</em>

For 2 x intercepts

y = x^3 - x

y  =(x-5)^2)(x+7)

Equate y to 0

(x-5)^2(x+7) = 0

Expand

(x-5)(x-5)(x+7) = 0

<em>x= 5 or x = -7</em>

For 1 x intercept

y = x^3

Equate y to 0

x^3 = 0

Take cube roots of both sides

x = 0

It has been shown above that a cubic function may have 1, 2 or 3.

So, I agree to the statement

For the quadratic function

A quadratic function will not have any x intercept when the function can not be factorized;

E.g.

y = x^2 + x + 17

<em>The above function has no x intercept.</em>

A quadratic function will have at least 1 x intercept when the function can be factorized;

E.g.

y = x^2- 6x + 9

Equate y to 0

x^2- 6x + 9 = 0

Expand

x^2 - 3x - 3x + 9 = 0

(x - 3)(x-3) = 0

x = 3

We've shown that a quadratic may have no x intercept, and it may also have x intercept(s)

Hence, I agree to both statement

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oksano4ka [1.4K]

Answer:

x= -2, y = -3

Step-by-step explanation:

1. substitute x = 4+2y in the first equation: \begin{bmatrix}2\left(4+2y\right)+y=-7\end{bmatrix}

simplify it : \begin{bmatrix}8+5y=-7\end{bmatrix}

2. isolate y in 8 + 5y = -7 --> 5y = -7 - 8 -->

3. solve for y:  5y = -15 --> y = -15/5 --> y= -3

4. solve for x: x = 4 + 2y

x = 4 + 2(-3)

x = 4 + (-6)

x = -2

6 0
2 years ago
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6 0
3 years ago
Solve 12x-5&gt;-2 please
Stells [14]

Answer:

x >  \frac{1}{4}

Step-by-step explanation:

12x - 5 >  - 2

Lets add +5 in both the sides.

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=  > 12x > 3

Now lets divide 12 on both the sides.

=  >  \frac{12x}{12}  >  \frac{3}{12}

=  > x >  \frac{1}{4}

8 0
3 years ago
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\frac{a^n}{a^m}=a^{n-m}

Then:

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Therefore:

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7 0
8 months ago
Plz help me with these, I don't understand this subject.
Stolb23 [73]

Answer:

A

Step-by-step explanation:

I might be wrong but it seems right.

4 0
2 years ago
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