[size=150]Evaluate each expression for [math]a=9[/math], [math]b=-5[/math], and [math]c=-2[/math][br][/size][br][math]-b[/math]

[math]b^2[/math]

[math]b^2-4ac[/math]

[math]-b\pm\sqrt{a}[/math]

[list][size=150][*]Solve 1–2 equations by using the quadratic formula.[br][/*][*]Then, find and describe the error(s) in the worked solutions of the same equations as the ones you solved.[/*][/size][/list][br][table][tr][td]Equation 1: [math]\quad2x^2+3=8x[/math][/td][td]Equation 2: [math]\quad x^2+3x=10[/math][/td][/tr][tr][td]Equation 3: [math]\quad9x^2-2x-1=0[/math][/td][td]Equation 4: [math]\quad x^2-10x+23=0[/math][/td][/tr][/table][size=150][br]Here are the worked solutions with errors:[/size][br][br][table][tr][td]Equation 1:[math]\quad2x^2+3=8x[/math][/td][td]Equation 2:[math]\quad x^2+3x=10[/math][/td][/tr][tr][td][math]a=2,\, b= \text-8,\, c=3[/math][br][br][math]x=\frac{\text{-}b \pm \sqrt{b^2-4ac}}{2a} \\[br]x=\frac{\text{-}(\text{-}8) \pm \sqrt{(\text{-}8)^2-4(2)(3)}}{2(2)}\\ [br]x=\frac{8 \pm \sqrt{64-24}}{4}\\[br]x=\frac{8 \pm \sqrt{40}}{4}\\[br]x =2 \pm \sqrt{10}[/math][br][/td][td][math]a=1,b=3,c=10[/math][br][br][math]x=\frac{\text{-}b \pm \sqrt{b^2-4ac}}{2a}\\ [br]x=\frac{\text{-}3 \pm \sqrt{3^2-4(1)(10)}}{2(1)}\\ [br]x=\frac{\text{-}3 \pm \sqrt{9-40}}{2}\\ [br]x=\frac{\text{-}3 \pm \sqrt{\text{-}31}}{2}\\ [br]\text{No solutions}[/math][br][/td][/tr][tr][td][br]Equation 3:[math]\quad9x^2-2x-1=0[/math][/td][td][br]Equation 4:[math]\quad x^2-10x+23=0[/math][/td][/tr][tr][td][math]a = 9,\,b = \text-2,\, c = \text-1[/math][br][br][br][math]x=\frac{\text{-}b \pm \sqrt{b^2-4ac}}{2a}\\ [br]x=\frac{2 \pm \sqrt{(\text{-}2)^2-4(9)(\text{-}1)}}{2}\\ [br]x=\frac{2 \pm \sqrt{4+36}}{2}\\[br]x=\frac{2 \pm \sqrt{40}}{2}[/math][/td][td][math]a = 1,\,b = \text-10,\, c = 23[/math][br][br][math]x=\frac{\text{-}b \pm \sqrt{b^2-4ac}}{2a}\\ [br]x=\frac{\text{-}10 \pm \sqrt{(\text{-}10)^2-4(1)(23)}}{2}\\ [br]x=\frac{\text{-}10 \pm \sqrt{\text{-}100-92}}{2}\\[br]x=\frac{\text{-}10 \pm \sqrt{\text{-}192}}{2}\\ [br]\text{No solutions}[/math][/td][/tr][/table]

[size=150]The equation [math]h\left(t\right)=2+30t-5t^2[/math] represents the height, as a function of time, of a pumpkin that was [br]catapulted up in the air. Height is measured in meters and time is measured in seconds.[/size][br][br][size=100]The pumpkin reached a maximum height of 47 meters. How many seconds after launch did that happen? Show your reasoning.[/size]

Suppose someone was unconvinced by your solution. Find another way (besides the steps you already took) to show your solution is correct.[br]

[size=150]The equation [math]r\left(p\right)=80p-p^2[/math] models the revenue a band expects to collect as a function of the price of one concert ticket. Ticket prices and revenues are in dollars.[br][/size][br][size=100]A band member says that a ticket price of either $15.50 or $74.50 would generate approximately $1,000 in revenue. Do you agree? Show your reasoning.[/size]

[size=150]Function [math]g[/math] is defined by the equation [math]g\left(t\right)=2+30t-5t^2-47[/math]. Its graph opens downward.[br][/size][br]Find the zeros of function [math]g[/math] without graphing. Show your reasoning.

Explain or show how the zeros you found can tell us the vertex of the graph of [math]g[/math].[br]

Study the expressions that define functions [math]g[/math] and [math]h[/math] (which defined the height of the pumpkin). Explain how the maximum of function [math]h[/math], once we know it, can tell us the maximum of [math]g[/math].[br]

[size=150]Mai and Jada are solving the equation [math]2x^2-7x=15[/math] using the quadratic formula but found different solutions.[/size][br][table][tr][td]Mai wrote:[/td][td]Jada wrote:[/td][/tr][tr][td][math]x = \frac{\text{-} 7 \pm \sqrt{7^2 - 4(2)(\text{-}15)}}{2(2)}\\ [br]x = \frac{\text{-} 7 \pm \sqrt{49 - (\text{-} 120)}}{4}\\ [br]x = \frac{\text{-} 7 \pm \sqrt{169}}{4}\\ [br]x = \frac{\text{-} 7 \pm 13}{4}\\ [br]x = \text{-} 5 \quad \text{ or } \quad x = \frac32[/math][/td][td][math]x = \frac{\text{-} (\text{-} 7) \pm \sqrt{\text{-} 7^2 - 4(2)(\text{-}15)}}{2(2)}\\ [br]x = \frac{7 \pm \sqrt{\text{-} 49 - (\text{-} 120)}}{4}\\ [br]x = \frac{7 \pm \sqrt{71} }{4}[/math][/td][/tr][/table][br]If this equation is written in standard form, [math]ax^2+bx+c=0[/math], what are the values of [math]a[/math], [math]b[/math], and [math]c[/math]?

Do you agree with either of them? Explain your reasoning.[br]

[size=150]The equation [math]h\left(t\right)=-16t^2+80t+64[/math] represents the height, in feet, of a potato [math]t[/math] seconds after it was launched from a mechanical device.[/size][br][br]Write an equation that would allow us to find the time the potato hits the ground.

Solve the equation without graphing. Show your reasoning.

[size=150]Priya found [math]x=3[/math] and [math]x=-1[/math] as solutions to [math]3x^2-6x-9=0[/math]. [/size][size=100][size=150]Is she correct? Show how you know. [/size][/size]

[size=150]Lin says she can tell that [math]25x^2+40x+16[/math] and [math]49x^2-112x+64[/math] are perfect squares because each expression has the following characteristics, which she saw in other perfect squares in standard form:[/size][list][size=150][*]The first term is a perfect square. The last term is also a perfect square.[/*][*]If we multiply a square root of the first term and a square root of the last term and then double the product, the result is the middle term.[/*][/size][/list][size=100]Show that each expression has the characteristics Lin described.[br][/size]

Write each expression in factored form.

[size=150]What are the solutions to the equation [math]2x^2-5x-1=0[/math]?[/size]

[math]x^2+11x+24=0[/math]

[math]4x^2+20x+25=0[/math]

[math]x^2+8x=5[/math]

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[/img][br][math]y=10\left(\frac{2}{3}\right)^x[/math]

[math]y=10\left(\frac{1}{4}\right)^x[/math]

[math]y=10\left(\frac{3}{5}\right)^x[/math]

[size=150]The function [math]f[/math] is defined by [math]f\left(x\right)=\left(x+1\right)\left(x+6\right)[/math].[/size][br][br]What are the [math]x[/math]-intercepts of the graph of [math]f[/math]?

Find the coordinates of the vertex of the graph of [math]f[/math]. Show your reasoning.[br]