What are the x-intercepts of the function f(x) = –2x2 – 3x + 20?

Question

This is hard to me . I cant get no help.

Answer 1

x-intercepts are at (0, x)

 

0 = -2x² - 3x + 20

0 = 2x² + 3x - 20          multiply both sides by -1

0 = (2x - 5)(x + 4)        FOIL

 

2x = 5                          zero product rule

x = 5/2

 

x = -4                           zero product rule

 

{-4, 5/2}

Answer 2

The x-intercepts of the function are the values for x which make f(x) = 0. Since this is a quadratic function, we can attempt to factor it and solve for the x values one by one. If that fails, we can always use the quadratic equation,

 

{-b ± [√(b2 - 4ac)]} / 2a .

 

 

Through check-and-guess means, we find that

 

-2x² - 3x + 20 = 0

 

factors out to 

 

(-2x + 5)(x + 4) = 0 .

 

We set both expressions equal to zero because we want the x values that give us a y value equal to zero.

 

Solving for x in the first factor, we find that

 

-2x + 5 = 0

 

so

 

-2x = -5

 

and

 

x = -5/-2 = 5/2 .

 

That's one x value that leads to y = 0. Since this is a quadratic function (highest exponent is 2), we know there are two x values total. There's one more left.

 

 

Solving for x in the second factor, we find that 

 

x + 4 = 0

 

so 

 

x = -4 .

 

So the two x-intercepts are x = 5/2  and x = -4.

 

We can double check these values by plugging them into our quadratic function one at a time. If they both give f(x) = 0, then they are in fact x-intercepts.

 

 

Plugging in x = 5/2, we get

 

-2(5/2)² - 3(5/2) + 20 = 0

 

-2(25/4) - (15/2) + 20 = 0

 

(-50/4) - (15/2) + 20 = 0

 

-12.5 - 7.5 + 20 = 0

 

-20 + 20 = 0

 

0 = 0

 

The statement is true, so x = 5/2 is an x-intercept of the function.

 

Next, plugging in x = -4, we get 

 

-2(-4)² - 3(-4) + 20 = 0

 

-2(16) + 12 + 20 = 0

 

-32 + 12 + 20 = 0

 

-20 + 20 =0

 

0 = 0

 

The statement is true, so x = -4 is an x-intercept of the function.