Solve the proportion.
2 answers:
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Answer:
(4, -25)
Step-by-step explanation:
One way to answer this is to put the equation into vertex form.
f(x)= x^2 -8x -9 . . . . . given
Add and subtract the square of half the x-coefficient:
f(x) = x^2 -8x +(-8/2)^2 -9 -(-8/2)^2
f(x) = x^2 -8x +16 -25
f(x) = (x -4)^2 -25
Comparing this to the vertex form of a quadratic:
f(x) = a(x -h)^2 +k
we find that (h, k) = (4, -25). This is the vertex.
_____
<em>Alternate solution</em>
The line of symmetry for ...
f(x) = ax^2 +bx +c
is given by x = -b/(2a). For your given quadratic that line is ...
x = -(-8)/(2(1)) = 4
Evaluating f(4) gives the y-coordinate:
f(4) = 4^2 -8·4 -9 = -25
The vertex is (x, y) = (4, -25).
Given the question "<span>Which algebraic expression is a polynomial with a degree of 2?" and the options:
1).
2).
3).
4).
A polynomial </span><span>is an expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables.
</span><span>The degree of a polynomial is the highest exponent of the terms of the polynomial.
For option 1: </span><span>It contains no fractional or negative exponent, hence it is a polynomial. But the highest exponent of the terms is 3, hence it is not of degree 2.
For opton 2: It contains a fractional exponent which violates the definition of a polynomial, hence, it is not a polynomial.
i.e.
For option 3: </span><span>It contains a negative exponent which violates the definition of a polynomial, hence, it is not a polynomial.
i.e.
For option 4: It contains no fractional or negative exponent, hence it is a polynomial. Also, the highest exponent of the terms is 2, hence it is of degree 2.
</span>
Therefore, <span> s a polynomial with a degree of 2. [option 4]</span>
1).
2).
3).
4).
A polynomial </span><span>is an expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables.
</span><span>The degree of a polynomial is the highest exponent of the terms of the polynomial.
For option 1: </span><span>It contains no fractional or negative exponent, hence it is a polynomial. But the highest exponent of the terms is 3, hence it is not of degree 2.
For opton 2: It contains a fractional exponent which violates the definition of a polynomial, hence, it is not a polynomial.
i.e.
For option 3: </span><span>It contains a negative exponent which violates the definition of a polynomial, hence, it is not a polynomial.
i.e.
For option 4: It contains no fractional or negative exponent, hence it is a polynomial. Also, the highest exponent of the terms is 2, hence it is of degree 2.
</span>
Therefore, <span>