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bezimeni [28]
3 years ago
8

A parabola has zeros at (5,0) and (-3,0) and passes through point (6,18) determine the axis of symmetry

Mathematics
1 answer:
worty [1.4K]3 years ago
5 0

Answer:

The axis of symmetry is x=1

Step-by-step explanation:

we know that

In a vertical parabola, the axis of symmetry is equal to the x-coordinate of the vertex

In this problem we have a vertical parabola open upward

The x-coordinate of the vertex is equal to the midpoint between the zeros of the parabola

so

x=\frac{5-3}{2}=1

therefore

The axis of symmetry is x=1

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<h2>Explanation:</h2>

A polynomial function in one variable is given by the form:

f(x)=a_{n}x^n+a_{n-1}x^{n-1}+\cdots +a_{2}x^2+a_{1}x+a_{0}

Since you haven't provided any expression, I'll choose the following function:

f(x)=x^{3}+3x^{2}+3

So this is indeed a polynomial function. A turning point is an x-value where we have either a local maximum or local minimum. So we need to take the derivative of this functions:

f'(x)=3x^2+6x \\ \\ Finding \ turning \ points: \\ \\ 3x^2+6x=0 \\ \\ x(3x+6)=0 \\ \\ \\ So: \\ \\ x=0 \\ \\  and \\ \\ \ 3x+6=0 \therefore \ \boxed{x=-2}

Conclusion:

  • <em>The graph of f is a polynomial function</em>
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<h2>Learn more:</h2>

Polynomial function: brainly.com/question/13729121

#LearnWithBrainly

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A gym employee is paid monthly. After working for three months, he earned $4,500. To determine how much money he will make over
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Last one anyone that can help me out?
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Part a. t = 7.29 years.

Part b. t = 27.73 years.

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Step-by-step explanation:

The formula for continuous compounding is: A = p*e^(rt); where A is the amount after compounding, p is the principle, e is the mathematical constant (2.718281), r is the rate of interest, and t is the time in years.

Part a. It is given that p = $2000, r = 2.5%, and A = $2400. In this part, t is unknown. Therefore: 2400 = 2000*e^(2.5t). This implies 1.2 = e^(0.025t). Taking natural logarithm on both sides yields ln(1.2) = ln(e^(0.025t)). A logarithmic property is that the power of the logarithmic expression can be shifted on the left side of the whole expression, thus multiplying it with the expression. Therefore, ln(1.2) = 0.025t*ln(e). Since ln(e) = 1, and making t the subject gives t = ln(1.2)/0.025. This means that t = 7.29 years (rounded to the nearest 2 decimal places)!!!

Part b. It is given that p = $2000, r = 2.5%, and A = $4000. In this part, t is unknown. Therefore: 4000 = 2000*e^(2.5t). This implies 2 = e^(0.025t). Taking natural logarithm on both sides yields ln(2) = ln(e^(0.025t)). A logarithmic property is that the power of the logarithmic expression can be shifted on the left side of the whole expression, thus multiplying it with the expression. Therefore, ln(2) = 0.025t*ln(e). Since ln(e) = 1, and making t the subject gives t = ln(2)/0.025. This means that t = 27.73 years (rounded to the nearest 2 decimal places)!!!

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