Question

How many times does the graph of 4x = 32 - x2 cross the x-axis? 0 1 2

Answer 1

Answer:

How many times does the graph of 4x = 32 - x2 cross the x-axis?

2

What are the solutions to the equation?  

✔ 4, -8

Step-by-step explanation:

Answer 2

Answer:

2

Step-by-step explanation:

4x = 32 - x2 would be much clearer if written as 4x = 32 - x^2.  Please use

" ^ " to indicate exponentiation.

Rewrite 4x = 32 - x^2 in the standard form of a quadratic:  x^2 + 4x - 32

Then the coefficients are a = 1, b = 4 and c = -32.

Find the discriminant.  It is b^2-4ac.  

Here, b^2-4ac = 4^2 - 4(1)(-32), or 16 + 128, or 144.

Because the discriminant is positive, we know immediately that this quadratic has two real, unequal roots.

So, the answer to this question is "the graph of 4x = 32 - x^2 cross the x-axis in two places."