How many times will the graph of y=3x^2-10 intersect the x-axis?
A. 0
B. 1
C. 2
D. 3
Idk plz help :(
The graph intersect the x-axis in points where x = 0
In this case:
3 x^2 - 10 =0
Add 10 to both sides
3 x^2 = 10
x^2 = 10 / 3
x = ± ✓( 10 / 3)
Answer C
Two times.
the discriminant is positive, so two roots
To determine how many times the graph of the equation y = 3x^2 - 10 intersects the x-axis, we need to consider the solutions for which y = 0. When the equation intersects the x-axis, y will be equal to zero.
We can solve for the intersections by setting y = 0:
0 = 3x^2 - 10
To solve this quadratic equation, we can either factor it or use the quadratic formula. Let's use the quadratic formula.
The quadratic formula is given by:
x = (-b ± sqrt(b^2 - 4ac)) / 2a
For our equation, a = 3, b = 0, and c = -10. Substituting these values into the quadratic formula, we have:
x = (-0 ± sqrt(0^2 - 4 * 3 * -10)) / (2 * 3)
x = (± sqrt(0 - (-120))) / 6
x = (± sqrt(0 + 120)) / 6
Simplifying further:
x = ± sqrt(120) / 6
x = ± sqrt(4*30) / 6
x = ± (2 * sqrt(30)) / 6
x = ± sqrt(30) / 3
We have two possible solutions for x, which are ± sqrt(30) / 3. This means that the graph intersects the x-axis at two different points.
Therefore, the answer is C. 2