graph the parabola y3x224x45Solutiony 3x2 24x 45 this is

graph the parabola y=-3x^2-24x-45

y = -3x² - 24x - 45

this is of the form y = ax² + bx + c

Here, a is negative, therefore the graph will be downwards parabola.

when x = 0, y will be:

y = - 3(0)² - 24(0) - 45

=> y = - 45

this is the y intercept of the graph. That is, the graph meets the y axis at co ordinates (0, - 45)

for x intercepts, substitute y = 0

therefore -3x² - 24x - 45 = 0

=> - [3x² + 24x + 45] = 0

=> 3x² + 24x + 45 = 0

=> 3x² + 9x + 15x + 45 = 0

=> 3x[x + 3] + 15[x + 3] = 0

=> [x + 3][3x + 15] = 0

=> x = - 3 and x = - 5

so the graph meets x axis at (- 3, 0) and (- 5, 0).

y = -3x² - 24x - 45

this can be written as:

y = - 3[x² - 8x] - 45

=> y = - 3[x² - 8x + 16] + 3

=> y = -3(x + 4)² + 3

therefore the vertex [highest point of the graph] is at x = - 4.