What is the vertex form, f(x) = a(x − h)2 + k, for a parabola that passes through the point (1, −7) and has (2, 3) as its vertex. what is the standard form of the equation? a. vertex form: f(x) = 10(x + 4)2 + 5 standard form: f(x) = −10x2 + 40x + 165 b. vertex form: f(x) = −6(x − 4)2 + 3 standard form: f(x) = −6x2 + 7x − 24 c. vertex form: f(x) = −10(x − 2)2 + 3 standard form: f(x) = −10x2 + 40x − 37 d. vertex form: f(x) = −3(x − 2)2 + 4 standard form: f(x) = −3x2 + 12x +16?

18

step-by-step explanation:

draw the shape and you will see that f and k are actually at adjacent vertices (points of the hexagon that are neighboring).   so find the distance between (1,2) and (4,2).   that is easy since (1,2) and (4,2) is just a vertical distance to count, which is 3.   it is a regular polygon which means all sides are congruent.   you have 6 sides (hexa) so multiply 6 by 3 to receive 18.

the largest number of the four options is 1.8 x 10-2

you have it in scientific notation.

1.80 x 10-6   = 0.00000180

1.80 x 10-4   = 0.000180 (bigger, or "less small", than the former one)

so

1.8 x 10-2       = 0.0180. as you see. the "less small", or the biggest one of them all.

as you have negative exponent, it means you are dividing 1.8 by 100 (i.e. moving the dot towards left, two times).

if you had positive exponent for the scientific notation, power of tenths, you would be multiplying times 100 (moving the dot towards right) as below:

1.8 x (10)2 = 180

so. if you have negative exponent in scientific notation, move the dot toward left. if it is positive, toward right as many times the exponent tells you.