Resourcesdown chevron
Testimonials
Plans
Sign in
Sign up
Resourcesright arrow
Testimonials
Plans
Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Amir stands on a balcony and throws a ball to his dog, who is at ground level. The ball's height (in meters above the ground), x seconds after Amir threw it, is modeled by: h(x)=-(x-2)^(2)+16 How many seconds after being thrown will the ball hit the ground? seconds

Amir stands on a balcony and throws a ball to his dog, who is at ground level. The ball's height (in meters above the ground), x x seconds after Amir threw it, is modeled by: h(x)=−(x−2)2+16 h(x) = -(x-2)^{2} + 16 How many seconds after being thrown will the ball hit the ground? seconds \text{seconds}

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Algebra 1right chevron icon
Solve quadratic equations: word problemsright chevron icon

Full solution

Q. Amir stands on a balcony and throws a ball to his dog, who is at ground level. The ball's height (in meters above the ground), x x seconds after Amir threw it, is modeled by: h(x)=−(x−2)2+16 h(x) = -(x-2)^{2} + 16 How many seconds after being thrown will the ball hit the ground? seconds \text{seconds}
  1. Understand the problem: We need to find the time when the ball's height is 00, which means when it hits the ground.
  2. Set height equation: Set the height equation equal to zero to find when the ball hits the ground.\newline0=−(x−2)2+160 = -(x-2)^2 + 16
  3. Solve equation for x: First, move the term 1616 to the other side of the equation to isolate the squared term. \newline−(x−2)2=−16-(x-2)^2 = -16 \newline(x−2)2=16(x-2)^2 = 16
  4. Take square root: Take the square root of both sides to solve for xx. \newline(x−2)2=16\sqrt{(x-2)^2} = \sqrt{16} \newlinex−2=±4x - 2 = \pm 4
  5. Solve for x: Solve for x by adding 22 to both possible values of the square root.\newlinex=2+4x = 2 + 4 or x=2−4x = 2 - 4\newlinex=6x = 6 or x=−2x = -2
  6. Interpret results: Since time cannot be negative, we discard the negative value.\newlineThe ball will hit the ground 66 seconds after being thrown.

More problems from Solve quadratic equations: word problems

Question
Solve for v v .\newlinev2+8v+12=0 v^2+8v+12=0\newlineWrite each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas.\newlinev= v=_____
Get tutor helpright-arrow

Posted 1 month ago

Question
Solve for u u .\newlineu2=9 u^2 = 9 \newlineWrite your answers as integers or as proper or improper fractions in simplest form.\newlineu= u = _____ or u= u = _____
Get tutor helpright-arrow

Posted 2 months ago

Question
Complete the square. Fill in the number that makes the polynomial a perfect-square quadratic.\newlinek2−20k+_____k^2 - 20k + \_\_\_\_\_
Get tutor helpright-arrow

Posted 2 months ago

Question
Solve by completing the square.\newlineu2−24u−23=0u^2 - 24u - 23 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newline`u` = ________ or `u` =______
Get tutor helpright-arrow

Posted 2 months ago

Question
Find the discriminant. \newline2q2−9q+8=02q^2 - 9q + 8 = 0\newline______
Get tutor helpright-arrow

Posted 2 months ago

Question
Solve the system of equations.\newliney=22x−38 y = 22x - 38 \newliney=x2+11x−14 y = x^2 + 11x - 14 \newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(_,_) (\_,\_) \newline(_,_) (\_,\_)
Get tutor helpright-arrow

Posted 1 month ago

Question
Solve for aa.\newline(a+5)(a+1)=0(a + 5)(a + 1) = 0\newlineWrite your answers as integers or as proper or improper fractions in simplest form.\newlinea=a = _____ or a=a = _____
Get tutor helpright-arrow

Posted 2 months ago

Question
Let p=x2−7 p=x^{2}-7 . Which equation is equivalent to (x2−7)2−4x2+28=5 (x^{2}-7)^{2}-4x^{2}+28=5 in terms of p p ? Choose 11 answer: \newline(A) p2−4p+23=0 p^{2}-4p+23=0 \newline(B) p2+4p−5=0 p^{2}+4p-5=0 \newline(C) p2−4p−5=0 p^{2}-4p-5=0 \newline(D) p2+4p+23=0 p^{2}+4p+23=0
Get tutor helpright-arrow

Posted 2 months ago

Question
Let m=2x+3m=2x+3. Which equation is equivalent to (2x+3)2−14x−21=−6(2x+3)^{2}-14x-21=-6 in terms of mm? Choose 11 answer: \newline(A) m2+7m+6=0m^{2}+7m+6=0 \newline(B) m2−7m−15=0m^{2}-7m-15=0 \newline(C) m2−7m+6=0m^{2}-7m+6=0 \newline(D) m2+7m−15=0m^{2}+7m-15=0
Get tutor helpright-arrow

Posted 2 months ago

Question
Let m=x2+3m=x^{2}+3. Which equation is equivalent to (x2+3)2+7x2+21=−10(x^{2}+3)^{2}+7x^{2}+21=-10 in terms of mm? Choose 11 answer:\newline(A) m2−7m+31=0m^{2}-7m+31=0\newline(B) m2+7m+31=0m^{2}+7m+31=0\newline(C) m2−7m+10=0m^{2}-7m+10=0\newline(D) m2+7m+10=0m^{2}+7m+10=0
Get tutor helpright-arrow

Posted 2 months ago

View all (42)