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Ana dives into a pool off of a springboard high dive. Her height (in meters above the water), x seconds after diving, is modeled by h(x)=-5(x+1)(x-3) How many seconds after diving will Ana hit the water? ◻ seconds

Ana dives into a pool off of a springboard high dive.\newlineHer height (in meters above the water), x x seconds after diving, is modeled by\newlineh(x)=−5(x+1)(x−3) h(x)=-5(x+1)(x-3) \newlineHow many seconds after diving will Ana hit the water?\newline□ \square seconds

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Full solution

Q. Ana dives into a pool off of a springboard high dive.\newlineHer height (in meters above the water), x x seconds after diving, is modeled by\newlineh(x)=−5(x+1)(x−3) h(x)=-5(x+1)(x-3) \newlineHow many seconds after diving will Ana hit the water?\newline□ \square seconds
  1. Set Equation to Zero: To find when Ana hits the water, we need to solve for xx when h(x)=0h(x) = 0.
    h(x)=−5(x+1)(x−3)h(x) = -5(x+1)(x-3)
    Set h(x)h(x) to 00 and solve for xx.
    0=−5(x+1)(x−3)0 = -5(x+1)(x-3)
  2. Simplify Equation: Divide both sides by −5-5 to simplify the equation.\newline0=(x+1)(x−3)0 = (x+1)(x-3)
  3. Set Factors Equal: Now, set each factor equal to zero and solve for xx.\newlinex+1=0 or x−3=0x+1 = 0 \text{ or } x-3 = 0
  4. Solve for x: Solve the first equation for x.\newlinex=−1x = -1
  5. Solve for x: Solve the second equation for x.\newlinex=3x = 3

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