Use the function f(x) to answer the questions:
f(x) = 2x2 - 5x+3
Part A: What are the x-intercepts of the graph of f(x)? Show your work.
To find the x-intercepts of the graph of f(x), we need to determine the values of x when f(x) equals zero.
Setting f(x) equal to zero, we have:
2x^2 - 5x + 3 = 0
We can now attempt to factor this quadratic equation. However, it is not easily factorable, so we can instead use the quadratic formula.
The quadratic formula states that for an equation of the form ax^2 + bx + c = 0, the solutions for x can be found by using the formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
For our equation, a = 2, b = -5, and c = 3. Substituting these values into the quadratic formula, we have:
x = (-(-5) ± √((-5)^2 - 4(2)(3))) / (2(2))
= (5 ± √(25 - 24)) / 4
= (5 ± √1) / 4
Therefore, we have two possible solutions for x:
1) When we take the positive square root:
x = (5 + 1) / 4
= 6 / 4
= 3/2
2) When we take the negative square root:
x = (5 - 1) / 4
= 4 / 4
= 1
So, the x-intercepts of the graph of f(x) are x = 3/2 and x = 1.
To find the x-intercepts of the graph of f(x), we need to set f(x) equal to zero and solve for x.
Given: f(x) = 2x^2 - 5x + 3
Step 1: Set f(x) equal to zero:
2x^2 - 5x + 3 = 0
Step 2: Factor the quadratic equation. If factoring is not possible, use the quadratic formula.
In this case, the equation can be factored as:
(2x - 3)(x - 1) = 0
Step 3: Set each factor equal to zero and solve for x:
2x - 3 = 0
x - 1 = 0
Solving for x in each equation:
For 2x - 3 = 0:
2x = 3
x = 3/2
For x - 1 = 0:
x = 1
Step 4: Write the solutions:
The x-intercepts of the graph of f(x) are x = 3/2 and x = 1.