The vertex of this parabola is at (2, -4). when the y-value is -3, the x-value is -3. what is the coefficient of the squared term in the parabola's equation?

A parabola is expressed by a quadratic equation that is either facing on the right, left, upward or downward. Since the function given is opening to the left, then the standard form of the parabola equation is (y-k)^2 = -4a ( x-h) where (h,k) represents the coordinates of the vertex and a is the length of the latus rectum. The vertex is at (2,-4). Substituting, (y+4)^2 = -4a (x-2)

We can find a by substituting the other coordinate, (-3,-3). This is equal to 
(-3+4)^2 = -4a (-3-2)
1 = -4a (-5)
4a = 1/5

Hence the formula becomes (y+4)^2 = -1/5 (x-2)

The coefficient of the squared term hence is 5 as we multiply the whole equation by 5 to convert to standard form.

Intersecting secant-tangent theorem states that if a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.so to break it down: 1. pq acts as the tangent and ps as the secant with an intersection at p.sr = 21rp = 3x + 3pq = 4x + 4following to equation: tangent squared = the two segments multiplied by each otherso (4x + 4) ^ 2 = (3x + 3) • (21) simplifies to 16x^2 - 31x - 47 = 0 or (16x - 47)(x + 1) x = -1 or x = 47/162. pq acts as the tangent and ps as the secant with an intersection at p (again! )sr = 16rp = xpq = 15(15) ^ 2 = 16 • x225 = 16xx = 225/163. the interesting chords are proportional to each other so a ratio is possible to set up: ap dp 10 3 + x = = —— = pc pb 8 xcross multiple to get 10x = (3 + x)(8)x = 12