Question

problem: the football travels in a parabolic path defined by this equation: y = -0.1x² + 4x lets find how long a field goal this kicker could make. substitute y = 10 into the equation to find the length, in yards, of a successful field goal. y = -0.1x² + 4x 10 = -0.1x² + 4x use the quadratic formula to find x, the length, in yards, of a successful field goal. round to the nearest hundredth. enter the correct answer. done

Explanation:

Step1: Rearrange to standard quadratic form

$0.1x^2 - 4x + 10 = 0$
Multiply by 10 to eliminate decimals:
$x^2 - 40x + 100 = 0$

Step2: Identify quadratic coefficients

For $ax^2+bx+c=0$, $a=1$, $b=-40$, $c=100$

Step3: Apply quadratic formula

Quadratic formula: $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$
Substitute values:
$x=\frac{40\pm\sqrt{(-40)^2-4(1)(100)}}{2(1)}$

Step4: Calculate discriminant

$\sqrt{1600-400}=\sqrt{1200}=20\sqrt{3}\approx34.641$

Step5: Solve for x values

$x=\frac{40+34.641}{2}\approx37.32$, $x=\frac{40-34.641}{2}\approx2.68$
We discard the smaller value as it represents the start of the kick; the field goal length is the larger x.

Answer:

37.32 yards