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natali 33 [55]
3 years ago
13

What is the vertex and the equation of the axis of symmetry of the graph of y=x2-6x-7?

Mathematics
2 answers:
seraphim [82]3 years ago
5 0

Answer:

The vertex is<u> (3,-16)</u>  and axis of symmetry is <u>3</u>

Step-by-step explanation:

The vertex of a quadratic equation f(x)=ax^{2}+bx+c is calculated as (\frac{-b}{2a},f(\frac{-b}{2a}))

and the axis of symmetry is  \frac{-b}{2a}

Compare equation y=x^{2}-6x-7 with f(x)=ax^{2}+bx+c

Where a= 1 and b = -6

so, x=\frac{-b}{2a}=\frac{-(-6)}{2}

      x=3

Now, put the value of x=3 in y=x^{2}-6x-7

y=(3)^{2}-6(3)-7

y=9-18-7

y=-16

Therefore, the vertex is<u> (3,-16)</u>  and axis of symmetry is <u>3</u>

Ray Of Light [21]3 years ago
3 0
X= -b over 2a = --6 over 2×1=3
y=3²-6(3)-7=-16
vertex is (3,-16)
axis of symmetry is 3
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F(x) =x2+2x-3 g(x)=3x-14
Leviafan [203]

The solution to the composite function f(g(x)) is 9x² - 78x  + 165.

<h3>What is composite function?</h3>

A composite function is generally a function that is written inside another function.

Function composition is an operation that takes two functions f and g, and produces a function h = g ∘ f such that h(x) = g.

From the given composite function, the solution is determined as follows;

to solve for f(g(x)), we use the following methods.

f(x) = x² + 2x - 3, g(x) = 3x - 14

f(g(x)) = (3x - 14)² + 2(3x - 14) - 3

         = 9x² - 84x + 196  + 6x - 28 - 3

         = 9x² - 78x  + 165

Thus, the solution to the composite function f(g(x)) is 9x² - 78x  + 165.

Learn more about composite function here: brainly.com/question/10687170

#SPJ1

The complete question is below:

F(x) =x2+2x-3 g(x)=3x-14, find f(g(x))

8 0
1 year ago
The square of a number plus three times the number is 70. find the numbers.
Harrizon [31]

Answer:

Step-by-step explanation:

The equation for that is

x^2+3x=70

If we subtract over the 70, we have a quadratic that we can factor to solve for the values of x that will make that equation true.

x^2+3x-70=0

Now we need the factors of 70 that will either add or subtract to give us the linear term of 3. The factors of 70 that will work are 10 and 7. 10 times 7 is 70, and 10 - 7 = 3:

x^2+10x-7x-70=0 and now we will factor by grouping:

(x^2+10x)-(7x-70)=0 and factor out what's common:

x(x+10)-7(x+10)=0

The factor (x + 10) is common, so we will now factor that out:

(x+10)(x-7)=0

By the Zero Product Property, either x + 10 = 0 or x - 7 = 0, so x = -10 or 7

Those are the 2 numbers that will work.

(-10)^2+3(-10)=70 simplifies to

100 - 30 which does in fact equal 70. OR

(7)^2+3(7)=70 which simplifies to

49 + 21 which also equals 70.

So you're done!

3 0
3 years ago
A home has a room with length 22 feet and width 25 ft.
Elena L [17]

Answer:

O length = 11 inches width = 12.5 inches

Step-by-step explanation:

8 0
3 years ago
Anyone mind helping me out?
Igoryamba

Answer:

611 square miles

Step-by-step explanation:

Area of triangle = (1/2)*a*b*sinC (formula when u are not given the height of the triangle, but u are given with the angle.)

= (1/2)*30*47*sin(60°)

= 610.54 square miles (2 d.p)

≈611 square miles (rounded to nearest mile)

:)

4 0
3 years ago
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grin007 [14]

Answer:

ABC- Isoceles DEF- Scalene GHI- Equilateral

Step-by-step explanation:

I think for the first part you just pick shapes from your room that have the same equal/unequal sides as the triangle

8 0
3 years ago
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