A ball is thrown from an initial height of 3 meters with an initial upward velocity of 13 m/s. The ball's height h

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

Please help ASAP it’s due in 4 minutes

maxonik [38]

Answer:

a) well we know the hypotenuse and we know that all sides are 90 degrees, and that its an even square, so if we split it into a triangle , we know that the other 2 angles are 45 degrees total, with this we can calculate the other 2 sides, which round to 10 inches.

b) if we know the sides of the first side, knowing the fact that its a square we know that all sides are even, therefore, all sides are 10 inches, the formula the finding the perimeter is basic:

P=L(2) + W(2)

L being length, W being width and P being perimeter

so we add up all 4 sides, here is the equation:

10 + 10 + 10 + 10 = 10 x 4 = 40

With this, we know that the perimeter is 40 inches total

c) knowing how long the sides are, we can figure out the area through another basic formula:

A=L X W

With A meaning Area

since its a square, we know all the sides are even, so the width and length are both 10...

10 X 10 = 100

Step-by-step explanation:

I Hope I Helped!

3 0

3 years ago

C.) 4. Solve the system of equations

raketka [301]

You can set them equal to each other so -3x+4=4x-10 and then you add 3x and 10 on both sides and get7x=14 and then divided both sides by 7 and get x = 2 and check by plugging in and you get -2 for y on both so solution is x=2

7 0

2 years ago

scarlet is trying to find the height of a dam. she stands 90 meters away from the dam and records the angle of elevation to the

Harlamova29_29 [7]

Make a drawing with a right triangle.

The opposite side, y, is the height of the dam less 1.65 m

The base or adjacent side is 90 m

The angle between the two sides is 90 m.

Then tan (26) = y / 90

y = 90 tan(26) = 90 (0.4877) = 43.90 m

The height of the dam is 43.90m + 1.65m = 45.55 m

5 0

3 years ago

DA−2qA=B^3 Solve for A

a_sh-v [17]

Answer:

$a=\frac{b^{3} }{d-2q}$

Step-by-step explanation:

i think

8 0

3 years ago