Question

Write the equation of the quadratic function with roots -9 and -3 and a vertex at(-6, -1)
GETS A MEDAL!!! plz plz help

Answer 1

@RagingSoulGoku

Answer 2

oh wow

Answer 3

this is hard

Answer 4

\[(x-9)(x-3)=x^2 -12x + 27\]

Answer 5

https://app130.studyisland.com/pics/198809num2.png

Figure KLMN and figure PQRS, shown below, are similar figures.


If KN = 9 cm, MN = 21 cm, RS = 42 cm, and PS = 18 cm, what is the scale factor of figure PQRS to figure KLMN?
A. 3

B. 1/2

C. 1/3

D. 2

Answer 6

Help plz

Answer 7

whaat is scale factor? Help

Answer 8

A polynomial \(P(x)\) with roots \(r_1,r_2,...,r_n\) can be written as \[P(x) = a(x-r_1)(x-r_2)...(x-r_n)\] where \(a\) is an arbitrary constant (usually 1) to make the curve pass through a given point, if needed.

That means your polynomial with roots \(x = -9\) and \(x = -3\) can be written as\[P(x) = a(x-(-9))(x-(-3)) = a(x+9)(x+3)\]

Now we know that when \(x = -6\) the value of the function is \(-1\) so we can solve for the value of \(a\):
\[P(x) = a(x+9)(x+3)\]\[-1=a(-6+9)(-6+3)=a(3)(-3) = -9a\]\[-1=-9a\]\[a=\frac{1}{9}\]Therefore, our polynomial with roots at \(x = -9, \,x=-3\) with vertex \((-6,-1)\) is \[P(x) = \frac{1}{9}(x+9)(x+3) = \frac{1}{9}(x^2+12x+27)\]And as you can see from the graph attached, that satisifies all the conditions.

Answer 9

For the second problem, identify two corresponding sides where you know the lengths of each one. The scale factor from the larger figure (PQRS) to the smaller (KLMN) is just the ratio of the corresponding side from PQRS to the same side on KLMN. There are two sides for which you know the length on both figures; using either pair will give you the correct answer.