Question

SOMEBODY PLZ!! ITS THE LAST DAY I DONT WANNA FAIL :*(

Part A: The function f(x) = −x2 − 7x + 30 shows the relationship between the vertical distance of a diver from a pool's surface f(x), in feet, and the horizontal distance x, in feet, of a diver from the diving board. What is a zero of f(x), and what does it represent?


Part B: Solve 9x2 + 3x − 2 = 0 by using an appropriate method. Show the steps of your work, and explain why you chose the method used.

Answer 1

Part A. Lest fin the zeros of our function first:

`f(x)=-x^2-7x+30`
Step 1. Set the right side of the function equal to 0:

`0=-x^2-7x+30`

`-x^2-7x+30=0`
Step 2. Multiply both sides of the equation by -1

`(-1)(-x^2-7x+30)=0(-1)`

`x^2+7x-30=0`
Step 3. Factor the left side:

`(x+10)(x-3)=0`
Step 4. Set each factor equal to 0 and solve for
`x`:

`x+10=0` and
`x-3=0`

`x=-10` and
`x=3`
Since distances can't be negative, the zero of our function is
`x=3`.
We can conclude that the zero
`x=3` represents that when the horizontal distance of the diver is 3 ft, he is is in the surface of the pool. In other words, his vertical distance is zero.

Part B. To factor our quadratic equation
`9x^2+3x-2=0`, we are going to use the method for simple cases because
`a \\eq 0`:
Step 1. Find tow numbers whose product is
`ac` and its sum is
`b`:
We know form our quadratic that
`a=9`,
`b=3`, and
`c=-2`, so
`ac=9(-2)=-18`.
We want tow numbers that multiply together to make -18, and add up to 3.
Those number are 6 and -3.
`(6)(-3)=-18` and
`6-3=3`
Step 2. Rewrite the middle term
`3x` using those numbers:

`9x^2+6x-3x-2=0`
Step 3. Factor the expression:

`(9x^2+6x)-(3x+2)=0`

`3x(3x+2)-(3x+2)=0`

`(3x+2)(3x-1)=0`