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3 years ago

F(x)=4x^2+4x-15 Write the function D in intercept form. Use this form to list the zeros of the function.

Mathematics

1 answer:

valentinak56 [21]3 years ago

8 0

Answer:

Zeros are x = 1.5, -2.5

Step-by-step explanation:

Given function is,

F(x) = 4x² + 4x - 15

= 4(x² + x - 3.75) [Since, intercept form of a quadratic equation is the factored form of the function]

F(x) = 4(x² + 2.5x - 1.5x - 3.75)

= 4[x(x + 2.5) - 1.5(x + 2.5)]

= 4(x - 1.5)(x + 2.5)

For 'x' intercepts,

f(x) = 0

4(x - 1.5)(x + 2.5) = 0

x = 1.5, -2.5

Therefore, zeros of the given function are x = 1.5, -2.5.

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Step-by-step explanation:

a. To find the height, we can use the triangle formed by the side that measures 15, the side that measures 9. and the height. The hypotenuse of the triangle(the longest side opposite of the right angle), is 15. We can then use the Pythagorean Theorem, which states that $a^2+b^2=c^2$ , where c is the hypotenuse, and a and b are the two other sides. In this case, we need to find a leg of the triangle, not the hypotenuse. What do we do? We can first call the height a, and rearrange the Theorem into $c^2-b^2=a^2$ . $15^2=225, 9^2=81,$ and $225-81=\sqrt{144}$ =12. Therefore, the height of the parallelogram is $\boxed{12}$

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4 years ago

Given the function f(x) x^2-2x/x^3 +9x^2-10x Find any holes, vertical asymptotes, and horizontal asymptotes there may be.

yulyashka [42]

Answer:

See below

Step-by-step explanation:

I assume you mean $f(x)=\frac{x^2-2x}{x^3+9x^2-10x}$ :

Holes: Since $f(x)=\frac{x^2-2x}{x^3+9x^2-10x}$ reduces to $f(x)=\frac{x(x-2)}{x(x^2+9x-10)}$ , then there is a hole at $x=0$ as $x$ exists in both the numerator and denominator (however, its limit as x approaches 0 is 1/5).

Vertical Asymptotes: If we further reduce $f(x)=\frac{x(x-2)}{x(x^2+9x-10)}$ to $f(x)=\frac{x-2}{(x+10)(x-1)}$ , then we see that there are vertical asymptotes at $x=-10$ and $x=1$