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3 years ago

What is the equation for the flight of the ball

Mathematics

1 answer:

notsponge [240]3 years ago

6 0

Answer:

Option 2.

Step-by-step explanation:

To solve this, let's first find the values given to us.

The two x-intercepts are (4, 0) and (12, 0).

The parabola opens downward, meaning the value of a should be negative.

The vertex is (8, 32).

We know it is 8 because the halfway point between the x-intercepts is 8.

We can already eliminate option 3 because option 3 has a positive value of a.

This leaves us with options 1, 2, and 4.

The easiest way to figure out which option is correct is to graph the remaining functions in a graphing calculator.

The graph of a function that meets all of the above values is the correct function.

After graphing all of the functions, option 2 was the only one that had a vertex of (8, 32). So, option 2 is correct.

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3 years ago

Use the discriminant to predict the nature of the solutions to the equation 4x-3x²=10. Then, solve the equation.

AleksandrR [38]

Answer:

Two imaginary solutions:

x₁= $\frac{2}{3} -\frac{1}{3} i\sqrt{26}$

x₂ = $\frac{2}{3} +\frac{1}{3} i\sqrt{26}$

Step-by-step explanation:

When we are given a quadratic equation of the form ax² +bx + c = 0, the discriminant is given by the formula b² - 4ac.

The discriminant gives us information on how the solutions of the equations will be.

If the discriminant is zero, the equation will have only one solution and it will be real
If the discriminant is greater than zero, then the equation will have two solutions and they both will be real.
If the discriminant is less than zero, then the equation will have two imaginary solutions (in the complex numbers)

So now we will work with the equation given: 4x - 3x² = 10

First we will order the terms to make it look like a quadratic equation ax²+bx + c = 0

So:

4x - 3x² = 10

-3x² + 4x - 10 = 0 will be our equation

with this information we have that a = -3 b = 4 c = -10

And we will find the discriminant: $b^{2} -4ac = 4^{2} -4(-3)(-10) = 16-120=-104$

Therefore our discriminant is less than zero and we know that our equation will have two solutions in the complex numbers.

To proceed to solve the equation we will use the general formula

x₁= (-b+√b²-4ac)/2a

so x₁ = $\frac{-4+\sqrt{-104} }{2(-3)} \\\frac{-4+\sqrt{-104} }{-6}\\\frac{-4+2\sqrt{-26} }{-6} \\\frac{-4+2i\sqrt{26} }{-6} \\\frac{2}{3} -\frac{1}{3} i\sqrt{26}$

The second solution x₂ = (-b-√b²-4ac)/2a

so x₂= $\frac{-4-\sqrt{-104} }{2(-3)} \\\frac{-4-\sqrt{-104} }{-6}\\\frac{-4-2\sqrt{-26} }{-6} \\\frac{-4-2i\sqrt{26} }{-6} \\\frac{2}{3} +\frac{1}{3} i\sqrt{26}$

These are our two solutions in the imaginary numbers.

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3 years ago