#1**+1 **

What do you need help with here? Graphing? Factoring? Finding the roots? You haven't made it clear.

TheXSquaredFactor
Aug 18, 2017

#3**+3 **

Factoring and tell whether the parabola opens up or down. Also Identify the minimum and how does the axis of symmetry relate to the x-intercepts?

y=x^2-4x-32

Note that the form is y = x^2 + bx + c

factoring and tell whether the parabola opens up or down. Also Identify the minimum and how does the axis of symmetry relate to the x-intercepts?

Since x^2 is positive and there is no negative in front of the y, term, this parabola opens upward

Factoring we have.... y = ( x - 8) ( x + 4)

Setting y = 0, we can find the x intercepts thusly : 0 = (x - 8) ( x + 4).....setting each of these factors to 0 and solving for x produces the x intercepts of x = 8 and x = -4

The minimum can be found thusly :

The x coordinate of the vertex is given by -b / [ 2a ] ....b = -4 and a = 1 .....so .... -b / [2a ] = -[ -4] / [ 2(1)] =

2

Now....we can find the y coordinate of the vertex by plugging this value into the function...so we have ...

y = (2)^2 - 4(2) - 32 = 4 - 8 - 32 = 4 - 40 = -36 .....and this is the minimum y value of the parabola

The axis of symmetry will be found between the intercepts and is given by adding the intercepts and dividing by 2....so we have ... [ 8 + -4 ] / 2 = 4 / 2 = 2.......so the axis of symmetry is x = 2....this is no coincidence.....the axis of symmetry will occur at the vertex which is ( 2 , - 36)

CPhill
Aug 18, 2017

#4**+2 **

Trouble factoring a quadratic? Easy when you realise that ----

The factors of the constant term add up to the value of the co-efficient of x

Here you have x^2 - 4x - 32. We want the factors of -32 that add up to -4 because that is the

co-efficient of x here.

factors of -32 are plus or minus16 and plus or minus 2

and plus or minus 8 and plus or minus 4. Since there is no way we can get - 4 from the sums of

plus or minus 16 and 2 we look at plus or minus 8 and 4. The only possible sum is -8 + 4.

So the factors are (x-8)(x+4) Try a few more and you'll soon get the technique.

frasinscotland
Aug 18, 2017