For the function y = 3x2 + 18x + 24 find the y-intercepts the y-intercept and the verdicts and the axis of symmetry
To find the y-intercept of a function, we can set x = 0 and solve for y.
For y = 3x^2 + 18x + 24, when x = 0:
y = 3(0)^2 + 18(0) + 24
y = 0 + 0 + 24
y = 24
So, the y-intercept is (0, 24).
To find the x-intercepts, we can set y = 0 and solve for x. However, looking at the equation, we can see that the discriminant (b^2 - 4ac) is negative. This means that the quadratic equation has no real solutions, so there are no x-intercepts.
The vertex form of the quadratic equation is y = a(x-h)^2 + k, where (h, k) represents the vertex. To find the axis of symmetry, we can use the formula x = -b/2a.
For y = 3x^2 + 18x + 24:
a = 3
b = 18
Axis of symmetry:
x = -18 / (2 * 3)
x = -18 / 6
x = -3
So, the axis of symmetry is x = -3.
In summary:
- The y-intercept is (0, 24).
- There are no x-intercepts.
- The axis of symmetry is x = -3.