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IRISSAK [1]
3 years ago
9

Find the vertex of the parabola whose equation is y = x^2 + 8x + 12.

Mathematics
2 answers:
horsena [70]3 years ago
4 0
The vertex<span> of a </span>parabola<span> is the point where the </span>parabola<span> crosses its axis of symmetry. If the coefficient of the x 2 term is positive, the </span>vertex<span> will be the lowest point on the graph, the point at the bottom of the “ U ”-shape.
</span><span>
The vertex of the parabola whose equation is y = x^2 + 8 x + 12 will be :
</span>(x , y) = (-4,-4)
Black_prince [1.1K]3 years ago
3 0

Answer:

The vertex of the parabola is (-4,-4).

Step-by-step explanation:

If a quadratic function is defined as

y=ax^2+bx+c              ... (1)

Then the vertex of the function is

Vertex=(\frac{-b}{2a},f(\frac{-b}{2a}))

The given function is

y=x^2+8x+12             .... (2)

From (1) and (2), we get a=1,b=8 and c=12.

\frac{-b}{2a}=\frac{-8}{2(1)}=-4

Substitute x=-4 in the given equation.

f(\frac{-b}{2a})=f(-4)=y=(-4)^2+8(-4)+12

y=16-32+12=-4

Therefore the vertex of the parabola is (-4,-4).

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What is the vertex of this parabola? y= 2x² + 4x +5
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Answer:

vertex = (- 1, 3 )

Step-by-step explanation:

Given a parabola in standard form

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x_{vertex} = - \frac{b}{2a}

y = 2x² + 4x + 5 ← is in standard form

with a = 2, b = 4, then

x_{vertex} = - \frac{4}{4} = - 1

Substitute x = - 1 into the equation for corresponding value of y, that is

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3 years ago
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aleksandrvk [35]

Answer:

Part 1) FG=4.4\ units

Part 2) EF=3.9\ units

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Step-by-step explanation:

step 1

Find the measure of length side FG

In the right triangle EFG

we know that

sin(27^o)=\frac{GE}{FG} ----> by SOH (opposite side divided by the hypotenuse)

substitute the given values

sin(27^o)=\frac{2}{FG}

FG=\frac{2}{sin(27^o)}=4.4\ units

step 2

Find the measure of length side EF

In the right triangle EFG

we know that

cos(27^o)=\frac{EF}{FG} ----> by CAH (adjacent side divided by the hypotenuse)

substitute the given values

cos(27^o)=\frac{EF}{4.4}

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7 0
4 years ago
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Two triangles are similar if the only difference between them is the size, this means that their internal angles must be the same. If we look at the picture the first triangle has one angle equal to 40 degrees, one equal to 80 degrees and the third one is unkown (x). The second triangle has one angle equal to 40 degrees, one equal to 60 degrees and the third one is unkown (y). The sum of the internal angles of a triangle must be equal to 180 degrees, with this information we can find the values of the missing angles. We have:

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