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 [tex]ax^2 + bx+ c[/tex]
Where a, b, c are constants
Now, let's arrange this equation in this form:
[tex]4x=32-x^2\\x^2+4x-32=0[/tex]
Where
a = 1
b = 4
c = -32
We need to know the discriminant to know nature of roots. The discriminant is:
[tex]D=b^2-4ac[/tex]
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:
[tex]D=b^2-4ac\\D=(4)^2 -4(1)(-32)\\D=144[/tex]
Certainly D > 0, so there are 2 distinct roots and cuts the x-axis twice.
We get the roots/solutions by factoring:
[tex]x^2+4x-32=0\\(x+8)(x-4)=0\\x=4,-8[/tex]
Thus,
The graph crosses the x-axis 2 times
The solutions are x = -8 & x = 4
