Final answer:
To find the points of intersection between the functions y = 4x^2 and y = 2x + 6, set the equations equal to each other and solve for x. Using the quadratic formula, we find two possible values for x: 3/2 and -1. Substituting these values into either equation gives the corresponding y values, resulting in the points of intersection (3/2, 9/2) and (-1, 4).
The correct option is A.
Step-by-step explanation:
To find the points of intersection between the functions y = 4x^2 and y = 2x + 6, we need to set the two equations equal to each other and solve for x.
4x^2 = 2x + 6
Next, rearrange the equation to bring all terms to one side:
4x^2 - 2x - 6 = 0
This is a quadratic equation. We can solve for x by factoring or using the quadratic formula.
Using the quadratic formula, we have:
x = (-b ± sqrt(b^2 - 4ac))/(2a)
Plugging in the values a = 4, b = -2, and c = -6, we get:
x = (-(-2) ± sqrt((-2)^2 - 4(4)(-6)))/(2(4))
Simplifying further gives:
x = (-(-2) ± sqrt(4 + 96))/(8)
x = (2 ± sqrt(100))/(8)
x = (2 ± 10)/(8)
x = 12/8 or -8/8
x = 3/2 or -1
Now, substitute the values of x into one of the original equations to find the corresponding y values. Plugging in x = 3/2 into either equation gives:
y = 4(3/2)^2 = 9/2
So, one point of intersection is (3/2, 9/2). Plugging in x = -1 into either equation gives:
y = 4(-1)^2 = 4
So, the other point of intersection is (-1, 4).