determine the x-intercept of the quadratic function

f(x)= 2x^2+ x-15

solve 2x^2 + x - 15 = 0

(2x - 5)(x + 3) = 0
x = 5/2 or x = -3

To determine the x-intercept of the quadratic function f(x) = 2x^2 + x - 15, we set f(x) equal to zero and solve for x.

Step 1: Set f(x) = 0
0 = 2x^2 + x - 15

Step 2: Factor the quadratic equation (if possible)
To factor the quadratic equation, we need to find two numbers that multiply to -30 (the product of the coefficients of x^2 and the constant term -15) and add up to the coefficient of x (which is 1 in this case).
The numbers that meet these criteria are 6 and -5.

0 = (2x + 6)(x - 5) (after factoring)

Step 3: Set each factor equal to zero and solve for x
First factor: 2x + 6 = 0
2x = -6
x = -3

Second factor: x - 5 = 0
x = 5

The x-intercepts of the quadratic function f(x) = 2x^2 + x - 15 are x = -3 and x = 5.

To determine the x-intercept of a quadratic function, you need to find the values of x when f(x) equals zero. In other words, you need to solve the quadratic equation 2x^2 + x - 15 = 0.

There are various methods to solve quadratic equations: factoring, completing the square, or using the quadratic formula. In this case, factoring may be the easiest method.

First, we need to factor the quadratic equation: 2x^2 + x - 15 = 0.

The factors can be written as (2x - 5)(x + 3) = 0.

Now, set each factor equal to zero and solve for x:

2x - 5 = 0 --> 2x = 5 --> x = 5/2 or 2.5.

x + 3 = 0 --> x = -3.

So, the x-intercepts of the quadratic function f(x) = 2x^2 + x - 15 are x = -3 and x = 2.5.