Respuesta :
Answer:
This parabola has 2 x-intercepts,
representing the times when the dolphin's height above water is 0 feet.
Step-by-step explanation:
the next answer is There are two real solutions
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This parabola has 0.3875 x-intercepts, representing the times when the dolphin's height above water is 0 feet.
Solve quadratic equation
The x-intercept is the point where the graph crosses the x-axis, which is when the value is y=0.
The calculation for y=0 would be
[tex]Y = -16x^{2} + 32x - 10[/tex]
[tex]0 = -16x^{2} + 32x - 10[/tex]
[tex]-8xx^{2} + 16x - 5=0[/tex]
Use the quadratic equation to solve the equation,
For a=-8, b=16, c=-5
[tex]$x_{1,2}=\frac{-16 \pm \sqrt{16^{2}-4(-8)(-5)}}{2(-8)}$[/tex]
[tex]$x_{1,2}=\frac{-16 \pm \sqrt{16^{2}-4(-8)(-5)}}{2(-8)}$[/tex]
[tex]$\sqrt{16^{2}-4(-8)(-5)}=4 \sqrt{6}$[/tex]
[tex]$x_{1,2}=\frac{-16 \pm 4 \sqrt{6}}{2(-8)}$[/tex]
Separate the solutions
[tex]$x_{1}=\frac{-16+4 \sqrt{6}}{2(-8)}, x_{2}=\frac{-16-4 \sqrt{6}}{2(-8)}$[/tex]
[tex]$x=\frac{-16+4 \sqrt{6}}{2(-8)}: \quad \frac{4-\sqrt{6}}{4}$[/tex]
[tex]$x=\frac{-16-4 \sqrt{6}}{2(-8)}: \frac{4+\sqrt{6}}{4}$[/tex]
The solutions to the quadratic equation are:
[tex]x=\frac{4-\sqrt{6}}{4}, x=\frac{4+\sqrt{6}}{4}[/tex]
Hence, [tex]x[/tex] =0.38762... or [tex]x[/tex]= 1.61237...
So, This parabola has 0.3875 x-intercepts, representing the times when the dolphin's height above water is 0 feet.
To learn more about solving quadratic equations, refer to:
https://brainly.com/question/8931342
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