Given the function f(x)=-7x^(2)-1, find the value of f((3)/(7)) in simplest form. Answer:

Identify Function & Value: Identify the function and the value to be substituted into the function. We are given the function f(x) = -7x^2 - 1 and we need to find the value of f((3)/(7)).Substitute x: Substitute x = (3)/(7) into the function. f((3)/(7)) = -7((3)/(7))^2 - 1Calculate Square: Calculate the square of (3)/(7). ((3)/(7))^2 = (3)^2 / (7)^2 = 9 / 49Multiply Result: Multiply the result by -7. -7 * (9 / 49) = -7 * 9 / 49 = -63 / 49Simplify Fraction: Simplify the fraction. -63 / 49 simplifies to -9 / 7 because both the numerator and the denominator are divisible by 7.Add Constant Term: Complete the calculation by adding the constant term from the function. f((3)/(7)) = (-9 / 7) - 1Convert to Fraction: Convert 1 to a fraction with a denominator of 7 to combine with -9 / 7. 1 = 7 / 7Add Fractions: Add the fractions. f((3)/(7)) = (-9 / 7) - (7 / 7) = (-9 - 7) / 7 = -16 / 7

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Given the function
f(x)=-7x^(2)-1, find the value of
f((3)/(7)) in simplest form.
Answer:

Given the function $f(x)=-7 x^{2}-1$ , find the value of $f\left(\frac{3}{7}\right)$ in simplest form. $\newline$ Answer:

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Algebra 2

Find the vertex of the transformed function

Full solution

Q. Given the function

f(x)=-7 x^{2}-1

, find the value of

f\left(\frac{3}{7}\right)

in simplest form.

\newline

Answer:

Identify Function & Value: Identify the function and the value to be substituted into the function. $\newline$ We are given the function $f(x) = -7x^2 - 1$ and we need to find the value of $f\left(\frac{3}{7}\right)$ .
Substitute $x$ : Substitute $x = \frac{3}{7}$ into the function. $f\left(\frac{3}{7}\right) = -7\left(\frac{3}{7}\right)^2 - 1$
Calculate Square: Calculate the square of $(\frac{3}{7})$ . $\left(\frac{3}{7}\right)^2 = \left(3\right)^2 / \left(7\right)^2 = \frac{9}{49}$
Multiply Result: Multiply the result by $-7$ . $\newline$ $-7 \times (\frac{9}{49}) = -7 \times \frac{9}{49} = \frac{-63}{49}$
Simplify Fraction: Simplify the fraction. $\newline$ $-63 / 49$ simplifies to $-9 / 7$ because both the numerator and the denominator are divisible by $7$ .
Add Constant Term: Complete the calculation by adding the constant term from the function. $f\left(\frac{3}{7}\right) = \left(-\frac{9}{7}\right) - 1$
Convert to Fraction: Convert $1$ to a fraction with a denominator of $7$ to combine with $-9 / 7$ . $\newline$ $1 = 7 / 7$
Add Fractions: Add the fractions. $\newline$ $f\left(\frac{3}{7}\right) = \frac{-9}{7} - \frac{7}{7} = \frac{-9 - 7}{7} = \frac{-16}{7}$