1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Galina-37 [17]
3 years ago
9

Y=-x^2+6x-4 Find the Axis of Symmetry and the Vertex, Also solve the whole equation.

Mathematics
1 answer:
Inessa [10]3 years ago
7 0

Answer:

1. <em>Axis of symmetry</em>: x = 3

2. <em>Vertex:</em> (3,5)

3. <em>Solution of the equation</em>:

<u />

  • x-intercepts:

               (3-\sqrt{5},0) \\\\(3+\sqrt{5},0)

  • y-intercept: (0, -4)

Explanation:

<u>1. Equation:</u>

    y=-x^2+6x-4

<u>2. </u><em><u>Axis of symmetry:</u></em>

That is the equation of a parabola, whose standard form is:

                 y=ax^2+bx+c

Where:    

                 a=-1;b=6;c=-4

The axis of symmetry is the vertical line with equation:

               x=-b/2a

Substitute  a=-1,\text{ and }b=6

          x=-6/[(2)(-1)]=-6/(-2)=3

Thus, the axis of symmetry is:

            x=3

<em><u>3. Vertex</u></em>

<em><u /></em>

The x-coordinate of the vertex is equal to the axys of symmetry, i.e x = 3.

To find the y-xoordinate, substitute this value of x into the equation for y:

               y=-x^2+6x-4\\\\y=-(3)^2+6(3)-4=-9+18-4=5

Therefore, the vertex is (3, 5)

<u>4. Find the x-intercepts</u>

The x-intercepts are the roots of the equation, which are the points wher y = 0.

        y=-x^2+6x-4=0

Use the quadratic equation:

       x=\frac{-b\pm \sqrt{b^2-4ac} }{2a} \\\\x=\frac{-6\pm\sqrt{(-6)^2-4(-1)(-4)} }{2(-1)}\\\\x_1=3-\sqrt{5} \\\\x_2=3+\sqrt{5}

<u>5. Find the y-intercept</u>

<u />

The y-intercet is the value of y when x=0:

         y=-x^2+6x-4\\\\y=-(0)^2+6(0)-4=-4

You might be interested in
What is the value of x?
vekshin1

Answer:

12, im pretty sure

Step-by-step explanation:

5 0
2 years ago
Please help me on this one question! (10th grade level)
Semmy [17]
Make an inequality representing both constraints.
0.5x+y<20
x+y≥24
for a
3 0
3 years ago
Read 2 more answers
What is the equation of the line passing through the points (–25, 50) and (25, 50) in slope-intercept form?
Tems11 [23]
The slope is 0, the equation is y=50
When the line is horizontal the slope is 0 and when the line is vertical the slope is undefined. 

6 0
2 years ago
Read 2 more answers
Coach Cranford bought bottled water for the basketball team. The bottles each hold 1 pint of water.
DaniilM [7]

Answer:

3 gallons of water

Step-by-step explanation:

1 gallon = 8 pints

24 pints of water (bottles) divided by 8 would be 3

therefore 24 pints of water is equivelant to 3 gallons of water.

4 0
2 years ago
3 days converted to seconds
Aleksandr [31]
259,200 seconds!!

hope this helps :)
8 0
3 years ago
Read 2 more answers
Other questions:
  • If you were to solve the following system by substitution, what would be the best variable to solve for and from what equation?2
    15·1 answer
  • 8(4 second power) +16
    12·2 answers
  • Sodium is a reactive metal. chlorine is a reactive gas. these two elements combine to form a
    10·1 answer
  • The number forty one to the power of negative start fraction two over five end fraction end power can be written in the form sta
    6·1 answer
  • What is the inverse of the function f(x)= 19/x³
    11·1 answer
  • Please help this is hard
    9·2 answers
  • Using complete sentences, describe how you would check the quotient of two rational expressions. Create and demonstrate your own
    11·1 answer
  • Which of the following is true regarding the solution to the logarithmic equation below? log Subscript 2 Baseline (x + 11) = 4.
    14·1 answer
  • Question 2
    5·1 answer
  • This is due today please help if you get it right you get brainliest if you get it!
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!