Y=3x^2+18x+24.
y-intercept?
X-intercept(s)?
Coordinates of the vertex?
Equation of axis of symmetry?
Maximum or minimum?
To find the y-intercept, set x to be 0 and solve for y:
y = 3(0)^2 + 18(0) + 24
y = 24
Therefore, the y-intercept is at (0, 24).
To find the x-intercepts, set y to be 0 and solve for x:
0 = 3x^2 + 18x + 24
0 = x^2 + 6x + 8
0 = (x + 2)(x + 4)
Therefore, the x-intercepts are at (-2, 0) and (-4, 0).
To find the coordinates of the vertex, we can use the formula x = -b/(2a) to find the x-coordinate first:
x = -18/(2*3)
x = -3
Now substitute x = -3 back into the equation to find the y-coordinate:
y = 3(-3)^2 + 18(-3) + 24
y = 3(9) - 54 + 24
y = 27 - 54 + 24
y = -3
Therefore, the vertex is at (-3, -3).
The equation of the axis of symmetry is given by x = -b/(2a), which in this case is x = -18/(2*3) = -3.
Since the coefficient of x^2 is positive (3), the parabola opens upwards and does not have a maximum but a minimum at the vertex.