Determine the equation of the graph and select the correct answer below.
y = (x + 3)^2 − 2y = (x − 3)^2 − 2y = (x + 3)^2 + 2y = (x − 3)^2 + 2

Let’s substitute x values of the minimum point of the graph into each equation and see which equation gives the correct equation ;
x = -3
y = 2
1. y = (x+3)^2-2
= (-3+3) ^2 -2
= 0^2 -2
= -2
Therefore first equation is wrong

2. y = (x-3)^2 -2
= (-3-3)^2 -2
y = 36-2
y = 34
Since y isn’t 34 the second equation is wrong

3. y = (x+3)^2 +2
= (-3+3)^2 +2
= 0^2 +2
= 2
Since y =2 the third equation is correct
Therefore third equation is correct

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