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Agata [3.3K]
3 years ago
13

Write the equation of the quadratic function in standard form represented by the graph.

Mathematics
1 answer:
algol133 years ago
6 0

Answer:

y = x^2 +6x+8

Step-by-step explanation:

First find the zeros, -4 ,-2

y =a (x - -4) (x - -2)

y = a(x+4)(x+2)

Then it is multiplied by a constant so pick a point on the curve and solve for the constant

We will use (0,8)

8 = a(0+4)(0+2)

8 = a(8)

a =1

y = (x+4)(x+2)

Writing in standard form

FOIL

y = x^2 +2x+4x+8

y = x^2 +6x+8

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Consider the function f(x)=-3x^2 +7x -k. [3 Marks] a) For what values of k will the function have no zeros? b) For what values o
Anna35 [415]

Answer: a) k >4.08

b) k = 4.08

c) k<4.08

Step-by-step explanation:

Since we have given that

f(x)=-3x^2+7x-k

a) For what values of k will the function have no zeros?

It mean it has no real zeroes i.e. Discriminant < 0

As we know that

D=b^2-4ac

Here, a =-3

b = 7

c = -k

So, it becomes,

D

b) For what values of k will the function have one zero?

It means it has one real root i.e equal roots.

So, in this case, D = 0

So, it becomes,

D=b^2-4ac=0\\\\D=7^2-4\times -3\times -k=0\\\\49-12k=0\\\\49=12k\\\\k=\dfrac{49}{12}\\\\k=4.08

c) For what values of k will the function have two zeros?

It means it has two real roots.

In this case, D>0

So, it becomes,

D=7^2-4\times -3\times -k>0\\\\49-12k>0\\\\-12k>-49\\\\12k

Hence, a) k >4.08

b) k = 4.08

c) k<4.08

3 0
3 years ago
Ralph is paid twice per month. His work offers a flexible-spending account to be used for medical expenses. This plan allows Ral
slava [35]
In this question, we're assuming Ralph had 0 in his saving funds to start with.

The glasses cost 1200 dollars.

There are 12 months in a year.

Each month, Ralph is given his check two times, that means that Ralph receives his check 2(12), or 24, times per year.

Divide 1200 (the cost of the glasses) by 24 (the amount of times Ralph is given his check)

1200 / 24
Divide both numerator and denominator by 12
100 / 2
Simplify
50

Ralph should have put 50 dollars per pay check to pay for the glasses.

A is your answer.

Have an awesome day! :)
6 0
3 years ago
A bakery sells 6350 muffins in 2010. The bakery sells 8310 muffins in 2015. Write a linear model that represents the number y of
krok68 [10]

Answer:

y = 6,350 + 392x

Step-by-step explanation:

3 0
3 years ago
Jones of Boston borrowed $40,000, 90 day, 10% note. After 60 days Jones made an initial payment of $6,000. Assuming the U.S. Rul
nadezda [96]
check a website called math-way without the dash it might help
6 0
3 years ago
Find the equation of the line given the slope and the y-intercept
GREYUIT [131]

Answer:

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

Step-by-step explanation:

The equation for a linear graph is usually written in the following format...

y = mx + b

Where m would be the slope, usually referring to rise over run and b would be the y-intercept (where the line crosses the y-axis). From the graph, we can see that the line crosses the y-axis at point 3 so b would be 3. The graph also shows us that for every 1 value that the line rises it moves to the right 2 values. Therefore, the slope would be 1/2. Using these values we can create the following equation...

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

7 0
3 years ago
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