A relation is a special type of function. A. True B. False (30) points

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

4 years ago

The value pie/2 is a solution for the equation 2sin^2x-sinx-1=0 true or false

Rasek [7]

Answer:

Yes, $\frac{\pi }{2}$ is a solution

Step-by-step explanation:

Recall that $sin(\frac{\pi }{2})=1$ . By replacing $\frac{\pi }{2}$ in the given trigonometric equation, we get 0 (zero) as a result, so this value is a solution:

$2*(sin(\frac{\pi }{2} ))^2-sin(\frac{\pi }{2})-1= 2*(1)^2-1-1=2-2=0$

6 0

3 years ago

postnew [5]

12-3=9 they switch up and it still equals the same thing

5 0

3 years ago

Read 2 more answers

A sample of students at a university took a test that diagnosed their learning styles as active or reflective and also as visual

anastassius [24]

Answer:

Kindly check explanation

Step-by-step explanation:

Given that :

Sample size, n = 39

Correlation Coefficient, r = 0.273

The hypothesis test to examine if there is a positive correlation :

H0 : ρ = 0

If there is a positive correlation, then ρ greater than 1

H0 : ρ > 1

The test statistic :

T = r / √(1 - r²)/(n - 2)

T = 0.273 / √(1 - 0.273²)/(39 - 2)

T = 0.273 / 0.1581541

T = 1.726

The Pvalue using a Pvalue calculator can be be obtained using df = n - 2, df = 39 - 2 = 37

The Pvalue = 0.0463

α= .10 and α= .05

At α= .10

Pvalue < α ; Hence, we reject H0 and conclude that a positive correlation exists

At α= 0.05 ;

Pvalue < α ; Hence, we reject H0 and conclude that a positive correlation exists

3 0

3 years ago

Please I need help with this!!!!!!

Bezzdna [24]

Answer:

Step-by-step explanation:

1) Step 4: Marc has converted radical form to exponent form

Step 5: He has evaluated the value of the radical

3)

$x = \sqrt[3]{8}$

Here, 3 is index and 8 is radicand.

Prime factorize 8 and for every 3 numbers we can take one number outside the radical

Solution:

$x = \sqrt[3]{2*2*2}\\\\x = 2$

4) No,my equation does not have an extraneous solution.

My solution, satisfies the equation

3 0

3 years ago