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Math  /  Algebra

QuestionDetermine the coordinates of the (i) yy-intercept of the graph of y=−3(x+2)2−1y=-3(x+2)^{2}-1.

Studdy Solution

STEP 1

1. The equation y=−3(x+2)2−1 y = -3(x+2)^2 - 1 represents a quadratic function.
2. The y y -intercept occurs where the graph intersects the y y -axis.
3. At the y y -intercept, the value of x x is 0 0 .

STEP 2

1. Substitute x=0 x = 0 into the equation.
2. Simplify the expression to find the y y -coordinate.
3. State the coordinates of the y y -intercept.

STEP 3

Substitute x=0 x = 0 into the equation y=−3(x+2)2−1 y = -3(x+2)^2 - 1 :
y=−3(0+2)2−1 y = -3(0+2)^2 - 1

STEP 4

Simplify the expression:
y=−3(2)2−1 y = -3(2)^2 - 1 y=−3(4)−1 y = -3(4) - 1 y=−12−1 y = -12 - 1 y=−13 y = -13

STEP 5

The coordinates of the y y -intercept are:
(0,−13) (0, -13)
The coordinates of the y y -intercept are:
(0,−13) \boxed{(0, -13)}

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