Help on math thanks its due today so i need it!!

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

Inessa [10]

Answer:

1. Axis of symmetry: x = 3

2. Vertex: (3,5)

3. Solution of the equation:

x-intercepts:

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

y-intercept: (0, -4)

Explanation:

1. Equation:

$y=-x^2+6x-4$

2. Axis of symmetry:

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:

$x=3$

3. Vertex

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)

4. Find the x-intercepts

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:

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

5. Find the y-intercept

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

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

7 0

3 years ago

I put this into my calculator but it keeps coming out as "error" :/ not sure if it's just my calculator or something with the pr

Triss [41]

Your calculator says error because you cant have a square root of a negative number because there is no solution to that maybe recheck your equation and try again

8 0

3 years ago

Find the equation of this line

maksim [4K]

Y=1/3x + 2 as the y intercept is 2 and slope is 1/3

3 0

1 year ago

Read 2 more answers

a recipe calls for a total of 3 2/3 cups of flour and sugar. it the recipe calls for 1/4 cup of sugar, how much flour is needed?

zavuch27 [327]

Answer:

This is very detailed as I wish to make some principles about fractions clear.

3

5

12

Explanation:

This question boils down to

3

2

3

−

1

4

A fractions structure is that of:

count

size indicator of what you are counting

→

numerator

denominator

You can not directly add or subtract the counts (numerators) unless the size indicators (denominators) are the same.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Consider

3

2

3

Write as

3

+

2

3

Multiply by 1 and you do not change the value. However, 1 comes in many forms so you can change the way something looks without changing its true value

[

3

×

1

]

+

2

3

[

3

×

3

]

+

2

3

9

3

+

2

3

=

11

3

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Putting it all together

3

2

3

−

1

4

→

11

3

−

1

4

But the size indicators are not the same. I chose to make them become 12

11

3

−

1

4

→

[

11

3

×

1

]

−

[

1

4

×

1

]

→

[

11

3

×

4

]

−

[

1

4

×

3

]

→

44

12

−

3

12

Now we may subtract the counts

→

44

−

3

12

=

41

12

But this is the same as

12

+

12

+

12

+

5

12

=

1

2

+

2

1

2

+

2

1

2

+

5

12

=

3

5

12

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

The soccer team collector $800 at a carwash fundraiser they charge five dollars for small vehicles and $10 for large vehicles th

Nadusha1986 [10]

800 - 50 = 750
750 ÷ 5 =150
150 small vehicles were washed

7 0

3 years ago