[size=150]Let's try to find at least one solution to [math]x^2-2x-35=0[/math][/size].[br][br]Choose a whole number between 0 and 10.
Evaluate the expression [math]x^2-2x-35[/math], using your number for [math]x[/math].
[size=100]If your number doesn't give a value of 0, look for someone in your class who may have chosen a number that does make the expression equal 0.[/size] Which number is it?
[size=100]There is another number that would make the expression [math]x^2-2x-35[/math] equal 0. [/size][br]Can you find it?
[size=150]To solve the equation [math]n^2-2n=99[/math], Tyler wrote out the following steps. Analyze Tyler’s work. Write down what Tyler did in each step.[/size] [br][br][math]\begin {align} n^2-2n&= 99 &\qquad&\text{Original equation}\\\\n^2-2n-99&=0 &\qquad &\text{Step 1}\\\\ (n-11)(n+9)&=0 &\qquad&\text{Step 2} \\\\ n-11=0 \quad \text{or} \quad &n+9=0 &\qquad& \text{Step 3}\\\\ n=11 \quad \text{or} \quad &n=\text-9 &\qquad&\text{Step 4} \end {align}[/math]
[size=150]Solve each equation by rewriting it in factored form and using the zero product property. Show your reasoning.[br][br][math]x^2+8x+15=0[/math] [br][/size]
[math]x^2-10x-11=0[/math]
[math](x+4)(x+5)-30=0[/math]
Solve this equation and explain or show your reasoning.[br][br][math](x^2-x-20)(x^2+2x-3)=(x^2+2x-8)(x^2-8x+15)[/math]
What do you notice about the [math]x[/math]-intercepts of the graph?
What do the [math]x[/math]-intercepts reveal about the function?
[size=100]Solve [math]x^2-2x+1=0[/math] by using the factored form and zero product property.[/size][br]Show your reasoning. What solutions do you get?
Write an equation to represent another quadratic function that you think will only have one zero.