From the equation below, enter the value of the coefficient that represents $c$ in the standard form of a quadratic equation.
$f(x)=5 x^2-6 x-7$
Answer (2)
Identify the given quadratic equation: f ( x ) = 5 x 2 − 6 x − 7 .
Compare the given equation with the standard form f ( x ) = a x 2 + b x + c .
Identify the coefficients: a = 5 , b = − 6 , and c = − 7 .
State the value of the coefficient c : − 7 .
Explanation
Identifying the Quadratic Equation The given equation is f ( x ) = 5 x 2 − 6 x − 7 . We need to identify the coefficient c in the standard form of a quadratic equation, which is f ( x ) = a x 2 + b x + c .
Comparing with Standard Form Comparing the given equation f ( x ) = 5 x 2 − 6 x − 7 with the standard form f ( x ) = a x 2 + b x + c , we can identify the coefficients as follows:
a = 5 b = − 6 c = − 7
Finding the Value of c The coefficient that represents c in the standard form of the quadratic equation is − 7 .
Examples
Understanding quadratic equations is crucial in various fields, such as physics and engineering. For example, when analyzing the trajectory of a projectile, the height of the projectile can be modeled by a quadratic equation. The constant term 'c' in the equation represents the initial height of the projectile. By knowing the values of 'a', 'b', and 'c', we can accurately predict the projectile's path and landing point, which is essential in sports like baseball or in designing artillery systems.
The coefficient that represents c in the quadratic equation f ( x ) = 5 x 2 − 6 x − 7 is − 7 . This is identified by comparing the equation to the standard form, f ( x ) = a x 2 + b x + c . Thus, c = − 7 .
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