A parabola can be drawn given a focus of (4,-8) and a directrix of x = -4. What can be said about the parabola?

Mathematics

1 answer:

Pani-rosa [81]3 years ago

6 0

Answer:

It opens to the right and the vertex is at (0, -8).

The axis of symmetry is y = -8.

Step-by-step explanation:

The vertex is halfway between the directrix and the focus.

The focus is to the right of the directrix so the curve will open towards the right. The axis of symmetry is the line y = -8.

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Harry and Terry are each told to calculate 8 − (2 + 5). Harry gets the correct answer. Terry ignores the parentheses and calcula

dsp73

$\huge\textbf{Hey there!}$

$\large\textsf{8 - (2 + 5)}\\\large\textsf{= 8 - 2 + 5}\\\large\textsf{= 8 - \bf 7}\\\large\textsf{= \bf 1}$

$\large\textsf{8 - 2 + 5}\\\large\textsf{= \bf 6 }\large\textsf{+ 5}\\\large\text{= \bf 11 }$

$\large\textsf{= 1 - 11}\\\large\textsf{= -10}\\\\\\\huge\textbf{Therefore, your answer is: \boxed{\mathsf{-10}}}\huge\checkmark$

$\huge\textbf{Good luck on your assignment \&}\\\huge\textbf{enjoy your day!}$

~ $\frak{Amphitritr1040:)}$

4 0

2 years ago

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Which of the following is a polynomial with roots negative square root of 5, square root of 5, and 3?

Alex Ar [27]

Answer:

$x^{3}-3x^{2}-5x+15$

Step-by-step explanation:

The roots of the given polynomial are: $-\sqrt{5}, \sqrt{5}, 3$

Since, $-\sqrt{5}, \sqrt{5}, 3$ are the roots of the polynomial, according to the factor theorem, $(x - (-\sqrt{5})), (x-\sqrt{5}), (x-3)$ would be the factors of the polynomial.

Since we have the factors of the polynomial, we can multiply them to get the desired polynomial.

Let the polynomial be represented by P(x), so

$P(x) = (x - (-\sqrt{5}))(x-\sqrt{5})(x-3)\\\\ P(x)=(x +\sqrt{5})(x-\sqrt{5})(x-3)\\\\ P(x)=(x^{2}-(\sqrt{5} )^{2})(x-3)\\\\ P(x)=(x^{2}-5)(x-3)\\\\ P(x)=x^{3}-3x^{2}-5x+15$