Determine the x-intercept(s) of the quadratic function .
E) no x-intercept(s)

Question

Determine the x-intercept(s) of the quadratic function  .
E) no x-intercept(s)

Quizplus · Accepted Answer

To find the x-intercept(s), we need to set the function equal to zero and solve for x.

11eb11e8_19c2_70a5_ad38_e992a158f173_TB4588_11 = ax^2 + bx + c

Setting it equal to zero:

ax^2 + bx + c = 0

Substituting the given function:

11eb11e8_19c2_70a5_ad38_e992a158f173_TB4588_11 = a(0)^2 + b(0) + c

11eb11e8_19c2_70a5_ad38_e992a158f173_TB4588_11 = c

So, the x-intercept(s) occur when y = 0, which is equivalent to setting the function equal to zero:

ax^2 + bx + c = 0

Substituting the given function:

11eb11e8_19c2_70a5_ad38_e992a158f173_TB4588_11 = a(x^2) + b(x) + c

Setting it equal to zero:

a(x^2) + b(x) + c = 0

Substituting the coefficients of the given function:

11eb11e8_19c2_70a5_ad38_e992a158f173_TB4588_11 = (-0.269)x^2 + (0.531)x + 1.406

(-0.269)x^2 + (0.531)x + 1.406 = 0

Using the quadratic formula, we get:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

Substituting the coefficients:

x = (-0.531 ± sqrt(0.531^2 - 4(-0.269)(1.406))) / 2(-0.269)

x = (-0.531 ± sqrt(0.531^2 + 1.509)) / -0.538

x = (-0.531 ± 1.245) / -0.538

x = 0.985 or -4.289

Therefore, the function has two x-intercepts: 0.985 and -4.289.

The best choice is C.

Determine the X-Intercept(s) of the Quadratic Function