Question

Can someone tell me what the answer for this problem is? (and how you are able to get that answer)

Answer 1

`\bf y=\cfrac{1}{2}(x-7)(x-7)`

now, if you set y to 0, so you can solve for "x", you'll notice, you'll get 7 twice, you can see it from (x-7) twice there, it has that root twice.

so, when x = 7, y = 0, that's the x-intercept, or so-called a solution or zeros.

now, it happens twice though, so, that simply means, the root of 7 has a multiplicity of 2 and is an even multiplicity, and even number, and when that happens, the graph doesn't really cross the x-axis, it simply bounces off of it.

so the graph goes down down, gets to 7, bounces back up, well, it made a U-turn, that's the vertex, at 7,0 as well.

to find the y-intercept, simply set x = 0, let's do so


`\bf y=\cfrac{1}{2}(x-7)(x-7)\implies y=\cfrac{1}{2}(0-7)(0-7)\implies y=\cfrac{1}{2}(-7)(-7) \\\\\\ y=\cfrac{49}{2}\implies y=24.5`

so is at 0, 24.5

the stretch will be the coefficient in front of the function, in this case is 1/2, is stretches in relation to the y-axis by twice as much.