It is known that the vertex of the parabola is (- 2, - 3), and the analytic expression of the parabola is obtained through the origin (1) (2) and the intersection of the parabola and the X axis is obtained (3) Write directly when y

It is known that the vertex of the parabola is (- 2, - 3), and the analytic expression of the parabola is obtained through the origin (1) (2) and the intersection of the parabola and the X axis is obtained (3) Write directly when y

The analytic formula of the parabola is y = a (x + 2) ² - 3x = 0, y = 0 is substituted into 0 = 4a-3a = 3 / 4  the analytic formula of the parabola is y = 3 / 4 (x + 2) ² - 3 (2). Y = 0 is substituted into ¾ (x + 2) ² - 3 = 0 (x + 2) ² = 4x + 2 = ± 2  X1 = 0, X2 = - 4. The intersection of the parabola and the X axis (0,0), (- 4,0) (3). - 4

The three vertices of an equilateral triangle are all on the parabola y ^ 2 = 4x, and one of them is the origin of the coordinate, so s △ can be calculated
The answer is 48 root 3

Let one of the vertices be (x, 2 * root x)
Because it's an equilateral triangle
SO 2 * radical X / x = tan30 = radical 3 / 3
4/x=1/3
x=12
So the other two vertices are (12,4 times radical 3) and (12, - 4 times radical 3)
S △ = 12 * (4 times radical 3 + 4 times radical 3) / 2 = 48 times radical 3
The calculation was wrong just now