Sketching Quadratic Functions

 $y=x^{2\ }+3x\ +2$  Given this equation the curve should look like: 

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Answer explanation

When the x^2 term is positive the curve will look like a valley or happy face or opens upwards.

 $y=-x^{2\ }+2x\ +3$  Given this function the curve should look like:

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Answer explanation

For the function with -x^2 (i.e. the leading term is negative) the curve would look like a mountain, sad face or opens downwards.

Given  $y\ =\ \left(x+3\right)\left(x-4\right)$  this function is similar to which quadratic curve form below

•  $y\ =\ ax^2+bx\ +c$  

•  $y\ =a\left(x-p\right)^2+q$  

•  $y\ =\ a\left(x-m\right)\left(x-n\right)$  

Answer explanation

Yes, this is called the root form or the x-intercept form

Given $y=-\left(x-4\right)^2+3$  which quadratic curve form is this similar to?

•  $y=ax^2+bx+c$  

•  $y=a\left(x-p\right)^2+q$  

•  $y=a\left(x-m\right)\left(x-n\right)$  

Answer explanation

Yes, this is called the maximum/minimum form.

Given  $y\ =\ \left(x-3\right)\left(x-4\right)$  what are the x-intercepts?

•  $3\ and\ 4$  

•  $-3\ and\ -4$  

•  $-3\ and\ 4$  

•  $3\ and\ -4$  

Answer explanation

Yes, we need to take into account the minus (-) sign in the root form, y = (x - m) (x - n)

Given $y=\left(x-4\right)^2+3$  what is the maximum point (p,q)?

•  $\left(4\ ,\ 3\right)$  

•  $\left(-4\ ,\ 3\right)$  

•  $\left(4\ ,\ -3\right)$  

•  $\left(-4\ ,\ -3\right)$  

Answer explanation

Yes, we need to take into account the max/min form y = (x - p)^2 + q

 $y\ =\ \left(x-3\right)\left(x-4\right)$  Given this function it should look like:

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Answer explanation

Yes, because the overall equation is positive it looks like a happy face. 

 $y\ =\ -\left(x+2\right)\left(x-3\right)$  Given the function, it should look like...

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Answer explanation

Yes, because the overall equation is negative, the function should look like a sad face.

 $y=\left(x-3\right)^2+5$  Given this equation, the curve should look like...

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Answer explanation

Yes, because the overall equation is positive, the curve should look like a happy face.

 $y=-\left(x-7\right)^2+3$  Given this function, the graph should look like...

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Answer explanation

Yes, because the overall equation is negative, the curve should look like a sad face.