All categories

4 years ago

Diagram below shows the curve of a quadratic function

Mathematics

1 answer:

uranmaximum [27]4 years ago

3 0

Answer:

q = -8, k = 2.

r = -6.

Step-by-step explanation:

f(x) = (x - p)^2 + q

This is the vertex form of a quadratic where the vertex is at the point (p, q).

Now the x intercepts are at -6 and 2 and the curve is symmetrical about the line x = p.

The value of p is the midpoint of -6 and 2 which is (-6+2) / 2 = -2.

So we have:

f(x) = 1/2(x - -2)^2 + q

f(x) = 1/2(x + 2)^2 + q

Now the graph passes through the point (2, 0) , where it intersects the x axis, therefore, substituting x = 2 and f(x) = 0:

0 = 1/2(2 + 2)^2 + q

0 = 1/2*16 + q

0 = 8 + q

q = -8.

Now convert this to standard form to find k:

f(x) = 1/2(x + 2)^2 - 8

f(x) = 1/2(x^2 + 4x + 4) - 8

f(x) = 1/2x^2 + 2x + 2 - 8

f(x) = 1/2x^2 + 2x - 6

So k = 2.

The r is the y coordinate when x = 0.

so r = 1/2(0+2)^2 - 8

= -6.

You might be interested in

Solve this pleasee!!!!!!!!!!!

Sholpan [36]

Answer:

1) Solution (2,-3)

2) Solution (-1, $-\frac{3}{2}$ )

3) Solution ( $\mathbf{-\frac{1}{2},-\frac{5}{2}}$ )

Step-by-step explanation:

We need to solve equations using elimination

1) $2x+2y=-2\\3x-2y=12$

Let:

$2x+2y=-2--eq(1)\\3x-2y=12--eq(2)$

Adding both equations:

$2x+2y=-2\\3x-2y=12\\--------\\5x=10\\x=\frac{10}{5}\\x=2$

We get value of x = 2

Now, put value of x into equation 1 to find value of y

$2x+2y=-2\\Put\:x=2\\2(2)+2y=-2\\4+2y=-2\\2y=-2-4\\2y=-6\\y=-6/2\\y=-3$

So, we get y = -3

Solution (2,-3)

2) $4x-2y=-1\\-4x+4y=-2$

Let:

$4x-2y=-1--eq(1)\\-4x+4y=-2--eq(2)$

Adding both equations

$4x-2y=-1\\-4x+4y=-2\\------\\2y=-3\\y=\frac{-3}{2}$

We get: y= -3/2

Now find value of x by putting value of y in eq(1)

$4x-2y=-1\\Put\:y=\frac{-3}{2}\\4x-2( \frac{-3}{2})=-1\\4x+3=-1\\4x=-1-3\\4x=-4\\x=\frac{-4}{4}\\x=-1$

We get x = -1

Solution (-1, $-\frac{3}{2}$ )

3) $x-y=2\\x+y=-3$

let:

$x-y=2--eq(1)\\x+y=-3--eq(2)$

Add both equations:

$x-y=2\\x+y=-3\\-----\\2x=-1\\x=-\frac{1}{2}$

We get x = -1/2

Now, put value of x in equation 2

$x+y=-3\\-\frac{1}{2}+y=-3\\y=-3+ \frac{1}{2}\\y=\frac{-6+1}{2}\\y=\frac{-5}{2}$

We get y = -5/2

Solution ( $\mathbf{-\frac{1}{2},-\frac{5}{2}}$ )

7 0

3 years ago

A person is standing close to the edge on a 56 foot building and throws the ball vertically upward. The quadratic function h(t)=

Romashka [77]

Answer:

Part 1)

225 feet.

Part 2)

7 seconds.

Step-by-step explanation:

The height h(t) of the ball above the ground after t seconds is modeled by the function:

$h(t)=-16t^2+104t+56$

Part 1)

We want to determine the maximum height of the ball.

Notice that the function is a quadratic with a negative leading coefficient, so its maximum will be at its vertex point.

The vertex of a parabola is given by:

$\displaystyle \text{Vertex} = \left(-\frac{b}{2a}, f\left(-\frac{b}{2a}\right)\right)$

In this case, a = -16, b = 104, and c = 56.

Find the x- (or rather t-) coordinate of the vertex. So:

$\displaystyle t=-\frac{(104)}{2(-16)}=\frac{104}{32}=\frac{13}{4}=3.25\text{ seconds}$

In other words, the ball reaches its maximum height after 3.25 seconds.

To find the maximum height, substitute this value back into the function. Hence:

$\displaystyle h(3.25)=-16(3.25)^2+104(3.25)+56=225\text{ feet}$

The maximum height of the ball is 225 feet in the air.

Part 2)

We want to find the amount of time it took for the ball to hit the ground.

When the ball hit the ground, its height above the ground is zero. Therefore, we can set h(t) to 0 and solve for t:

$0=-16t^2+104t+56$

We can simplify a bit. Divide both sides by -8:

$0=2t^2-13t-7$

We can factor. Find two numbers that multiply to 2(-7) = -14 and add to -13.

-14 and 1 works! Therefore, split the second term into -14 and 1:

$\displaystyle 0=2t^2-14t+t-7$

Factor out a 2t from the first two terms and group the last two terms:

$0=2t(t-7)+(t-7)$

Factor by grouping:

$0=(2t+1)(t-7)$

Zero Product Property:

$2t+1=0\text{ or } t-7=0$

Solve for each case:

$\displaystyle t=-0.5\text{ or } t=7$

Since time cannot be negative, we can ignore the first case.

Therefore, it takes seven seconds for the ball to hit the ground.

6 0

3 years ago

A turkey was cooked at 300 f in the oven for 5 hours. the internal temperature rose from 35 f to 150 f. what was the average ris

ziro4ka [17]

What do you think the answer is? Tell me and I will help you some more! :)

4 0

4 years ago

3 - (2x - 5) < -4(x + 2)

DIA [1.3K]

Answer:

x < -8

Step-by-step explanation:

3 - (2x - 5) < -4(x + 2)

-2x + 8 < -4x - 8

-2x < -4x - 16

2x < -16

x < -8

Best of Luck!

7 0

3 years ago

Emily scores 22.5 points per coin. After collecting a total of 2 coins, how many points will Emily have scored in all?

aalyn [17]

Answer:

the answer should be 45.0

5 0

4 years ago

Read 2 more answers