Question

Find the smallest zero for the function h(x) = 4x^2 - 8x - 60.

x = [ ]

Answer 1

To find the zeros of a quadratic function, we need to set h(x) equal to 0 and solve for x:

h(x) = 4x^2 - 8x - 60

0 = 4x^2 - 8x - 60

Divide the entire equation by 4 to simplify:

0 = x^2 - 2x - 15

Now, we need to factor the quadratic equation:

0 = (x - 5)(x + 3)

Setting each factor equal to 0 gives us the solutions for x:

x - 5 = 0
x = 5

x + 3 = 0
x = -3

So, the zeros for the function h(x) are x = 5 and x = -3. The smaller zero is x = -3.