Question

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

Answer 1

Answer:

1st:2

2nd:4,-8

Step-by-step explanation:

Answer 2

Answer:

The graph crosses the x-axis 2 times

The solutions are  x = -8  &  x = 4

Step-by-step explanation:

Qaudratics are in the form $ax^2 + bx+ c$

Where a, b, c are constants

Now, let's arrange this equation in this form:

$4x=32-x^2\\x^2+4x-32=0$

Where

a = 1

b = 4

c = -32

We need to know the discriminant to know nature of roots. The discriminant is:

$D=b^2-4ac$

If

• D = 0 , we have 2 similar root and there is 2 solutions and that touches the x-axis
• D > 0,  we have 2 distinct roots/solutions and both cut the x-axis
• D < 0,  we have imaginary roots and it never cuts the x-axis

Let's find value of Discriminant:

$D=b^2-4ac\\D=(4)^2 -4(1)(-32)\\D=144$

Certainly D > 0, so there are 2 distinct roots and cuts the x-axis twice.

We get the roots/solutions by factoring:

$x^2+4x-32=0\\(x+8)(x-4)=0\\x=4,-8$

Thus,

The graph crosses the x-axis 2 times

The solutions are  x = -8  &  x = 4