Confused about the formula

draw a ray diagram to confirm your work.

I am & I can't get it to match up... They haven't given an exact height, they just say "at least 4 squares high" but between 4 squares & my cap I can't get it to that point.

You are on the right track in using the mirror equation to solve for the location of the image. However, there is a sign error in your calculation.

Let's go through the steps again:

The mirror equation is given by:
(1/-f) = (1/do) + (1/di)

Given that the focal length (f) is 10 cm, and the object distance (do) is 15 cm, we can substitute these values into the equation:
(1/-10) = (1/15) + (1/di)

Now, let's solve for the image distance (di):

(1/-10) = (1/15) + (1/di)

To simplify the equation, we need to find a common denominator. The common denominator in this case is 15 * di:

(di/-10) = (di/15) + (15/-10)

Multiplying both sides of the equation by the common denominator, we get:

(di * di) / -10 = (15 * di) + (-15 * (15))

Simplifying further:

(di * di) / -10 = 15di - 225

Multiply both sides of the equation by -10 to get rid of the fraction:

di * di = -150di + 2250

Rearranging the equation:

di * di + 150di - 2250 = 0

Now, we can solve this quadratic equation for di. You can use the quadratic formula or factoring to find the values of di. In this case, factoring is easier:

(di + 75)(di - 30) = 0

From this equation, we get two possible solutions for di: di = -75 or di = 30.

Since the image distance can't be negative for a convex mirror, the correct solution is di = 30 cm.

Therefore, the location of the image is 30 cm behind the convex mirror.

Note: The mirror equation assumes a positive value for the image distance (di) when the image is virtual or formed on the same side as the object. For a convex mirror, the image formed is always virtual and located on the same side as the object.