[size=150]The quadratic equation [math]x^2+7x+10=0[/math] is in the form of [math]ax^2+bx+c=0[/math]. What are the values of [math]a[/math], [math]b[/math], and [math]c[/math]?[/size]
In the third line, what might be a good reason for multiplying each side of the equation by 4?
[size=150]Complete the unfinished steps, and explain what happens in each step in the second half of the solution.[br][br]Substitute the values of [math]a[/math], [math]b[/math], and [math]c[/math] into the quadratic formula, [math]x=\frac{\text{-}b\pm\sqrt{b^2-4ac}}{2a}[/math], but do not evaluate any of the expressions.[/size][br] Explain how this expression is related to solving [math]x^2+7x+10=0[/math] by completing the square.
[size=150]Consider the equation [math]x^2-29=0[/math].[/size][br][br]Does the quadratic formula work to solve this equation? Explain or show how you know.[br]
Can you solve this equation using square roots? Explain or show how you know.
[size=150]Clare is deriving the quadratic formula by solving [math]ax^2+bx+c=0[/math] by completing the square.[br][br]She arrived at this equation: [math](2ax+b)^2=b^2-4ac[/math].[/size][br][br]Briefly describe what she needs to do to finish solving for [math]x[/math] and then show the steps.
[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(t)=4+12t-16t^2[/math], where [math]t[/math] is measured in seconds since the ball was thrown.[br][br][/size]Find the solutions to [math]6=4+12t+16t^2[/math] without graphing. Show your reasoning.[br]
What do the solutions say about the tennis ball?[br]
[size=150]Consider the equation [math]y=2x(6-x)[/math].[/size][br][br]What are the [math]x[/math]-intercepts of the graph of this equation? Explain how you know.
What is the [math]x[/math]-coordinate of the vertex of the graph of this equation? Explain how you know.
What is the [math]y[/math]-coordinate of the vertex? Show your reasoning.