Which is the equation of the parabola? coordinate plane with a parabola facing up with vertex at 4 comma 2, the point 4 comma 6 and a horizontal line going through 0 comma negative 2

y = one sixteenth(x − 4)2 + 2

y = one sixteenth(x + 4)2 − 2

y = −one sixteenth(x − 2)2 + 4

y = −one sixteenth(x + 2)2 − 4

y = one sixteenth(x − 4)^2 + 2

Step-by-step explanation:

If the parabola is written as:

y = a*x^2 + b*x + c

then if the graph opens up, then a must be positive, so we can discard the third and fourth options, we remain with:

y = 1/6*(x - 4)^2 + 2 = 1/6x^2 - (8/6)*x + (16/6 + 2)

y =  1/6*(x + 4)^2 - 2  =  1/6x^2 + (8/6)*x + (16/6 - 2)

the vertex (4, 2)

then

x = -b/2a = 4.

this means that a and b must be of different sign, then the only correct option can be:

y = 1/6*(x - 4)^2 + 2 = 1/6x^2 - (8/6)*x + (16/6 + 2)

where:

x-vertex  = (8/6)/(2/6) = 4 as we wanted.

when we evaluate this function in x = 4 we get

y = 1/6*( 4 - 4)^2 + 2 = 2.

So the correct option must be: y = one sixteenth(x − 4)2 + 2

clock

step-by-step explanation:

c.   x=2.4cm

step-by-step explanation:

similar triangles are triangles which have the same shape but not the same size. this means their angle measures are equal but their side lengths are not instead they are proportional. to solve, we will set up a proportion and solve.

a proportion is two equal ratios set equal to each other. we form the ratios by finding corresponding sides (sides which match to each other on both triangles by their position). out ratios will be one side of the small triangle over the corresponding side on the big triangle as shown below:

.

to solve the proportion, we'll cross multiply by multiplying numerator with denominator across the equal sign.