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Over [174]
3 years ago
12

A quadratic function is a function of the form y=ax^2+bx+c where a, b, and c are constants. Given any 3 points in the plane, the

re is exactly one quadratic function whose graph contains these points. Find the quadratic function whose graph contains the points (0, -2), (-5, -17), and (3, -17). Enter the equation below. Function: y = 0

Mathematics
1 answer:
pochemuha3 years ago
8 0

Answer:

The quadratic function whose graph contains these points is y=-x^{2}-2x-2

Step-by-step explanation:

We know that a quadratic function is a function of the form y=ax^{2}+bx+c. The first step is use the 3 points given to write 3 equations to find the values of the constants <em>a</em>,<em>b</em>, and <em>c</em>.  

Substitute the points (0,-2), (-5,-17), and (3,-17) into the general form of a quadratic function.

-2=a*0^{2}+b*0+c\\c=-2

-17=a*-5^{2}+b*-5+c\\c=-25a+5b-17

-17=a*3^{2}+b*3+c\\ c=-9a-3b-17

We can solve these system of equations by substitution

  • Substitute c=-9a-3b-17

-9a-3b-17=25a+5b-17\\-9a-3b-17=-2

  • Isolate a for the first equation

-9a-3b-17=-25a+5b-17\\a=\frac{b}{2}

  • Substitute a=\frac{b}{2} into the second equation

-9\left(-\frac{b}{2}\right)-3b-17=-2

  • Find the value of b

-9\left(-\frac{4b}{17}\right)-3b-17=-2\\ b=-2

  • Find the value of a

a=\frac{b}{2}\\  a=-1

The solutions to the system of equations are:

b=-2,a=-1,c=-2

So the quadratic function whose graph contains these points is

y=-x^{2}-2x-2

As you can corroborate with the graph of this function.

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Approximately 3.5 feet - Option B

Step-by-step explanation:

Imagine that you have this walkway around the garden, with dimensions 30 by 20 feet. This walkway has a difference of x feet between it's length, and say the dimension 30 feet. In fact it has a difference of x along both dimensions - on either ends. Therefore, the increases length and width should be 30 + 2x, and 20 + 2x, which is with respect to an increases area of 1,000 square feet.

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There can't be a negative width of the walkway, hence our solution should be ( in exact terms ) \frac{5\left(\sqrt{41}-5\right)}{2}. The approximated value however is 3.5081...or approximately 3.5 feet.

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