[size=150]Select [b]all[/b] the equations that have 2 solutions.[/size]
[size=150]A frog jumps in the air. The height, in inches, of the frog is modeled by the function [math]h\left(t\right)=60t-75t^2[/math], where [math]t[/math] is the time after it jumped, measured in seconds.[/size][br][br]Solve [math]60t-75t^2=0[/math]. What do the solutions tell us about the jumping frog?
[size=150]A tennis ball is hit straight up in the air, and its height, in feet above the ground, is modeled by the equation [math]f\left(t\right)=4+12t-16t^2[/math], where [math]t[/math] is measured in seconds since the ball was thrown.[/size][br][br]Find the solutions to the equation [math]0=4+12t-16t^2[/math].
What do the solutions tell us about the tennis ball?[br]
[math]\left(x+1\right)\left(7x+2\right)[/math]
[math]\left(8x+1\right)\left(x-5\right)[/math]
[math]\left(2x+1\right)\left(2x-1\right)[/math]
[math]\left(4+x\right)\left(3x-2\right)[/math]
[math](4x-1)(\underline{\hspace{1in}})[/math] and [math]16x^2-8x+1[/math]
[math](9x + 2)(\underline{\hspace{1in}})[/math] and [math]9x^2-16x-4[/math]
[math](\underline{\hspace{1in}})(\text{-}x + 5)[/math] and [math]-7x^2+36x-5[/math]
[size=150]The number of downloads of a song is a function, [math]f[/math], of the number of weeks, [math]w[/math], since the song was released. The equation [math]f\left(w\right)=100,000\cdot\left(\frac{9}{10}\right)^w[/math] defines this function.[br][/size][br]What does the number 100,000 tell you about the downloads?
What about the [math]\frac{9}{10}[/math]?
Is [math]f\left(-1\right)[/math] meaningful in this situation? Explain your reasoning.[br]
[size=100][size=150]Consider the equation [math]4x^2-4x-15=0[/math].[/size][br][br]I[/size][size=100]dentify the values of [math]a[/math], [math]b[/math], and [math]c[/math] that you would substitute into the quadratic formula to solve the equation.[/size][br]
[size=100]The solutions to the equation are [math]x=-\frac{3}{2}[/math] and [math]x=\frac{5}{2}[/math]. [/size]Do these match the values of the last expression you evaluated in the previous question?
[size=150]Describe the graph of [math]y=-x^2[/math]. [/size][br][br](Does it open upward or downward? Where is its [math]y[/math]-intercept? What about its [math]x[/math]-intercepts?)[br]
[size=150]Without graphing, describe how adding [math]16x[/math] to [math]-x^2[/math] would change each feature of the graph of [math]y=-x^2[/math]. (If you get stuck, consider writing the expression in factored form.)[br][/size][br]the [math]x[/math]-intercepts?
the [math]y[/math]-intercept?
the direction of opening of the U-shape graph?