Find the vertex of this parabola: y=-4x^2+8x-12

Mathematics

2 answers:

Radda [10]2 years ago

8 0

(1,-8) is the vertex

tatiyna2 years ago

4 0

<span>The vertex of the parabola is the highest or lowest point of the graph.

</span><span>y=-4x^2+8x-12 = -4 (x^2 -2x +3)

Lets work with this now: </span>x^2 -2x +3

x^2 -2x +3 -> what is the closeset perfect square?
x^2 -2x +1 = (x-1)^2
So
x^2 -2x +3 = (x-1)^2 +2

Replacing to original
y=-4x^2+8x-12 = -4 (x^2 -2x +3) = -4 ((x-1)^2 +2) = -4 (x-1)^2 - 8

The min or max point is where the squared part = 0
So when x=1 , y= -4*0-8=-8

This will be the max of the parabola as there is - for the highest factor (-4x^2)

The max: x=1, y= -8

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A company that makes? hair-care products had 7000 people try a new shampoo. Of the 7000 ?people, 42 had a mild allergic reaction

hram777 [196]

Answer: Percent of people who had a mild allergic is 0.6%.

Step-by-step explanation:

Since we have given that

Total number of people try a new shampoo = 7000

Number of people had a mild allergic reaction = 42

We need to find the "Percentage of people had a mild allergic":

Percentage of people had a mild allergic is given by

$\frac{\text{ Total number of people who had a mild allergic}}{\text{ Total number of people}}\times 100\\\\=\frac{42}{7000}\times 100\\\\=\frac{42}{70}\\\\=0.6\%$