  We study electrically charged, static, spherically symmetric black holes in
quadratic gravity using the conformal-to-Kundt technique, which leads to a
considerable simplification of the field equations. We study the solutions
using a Frobenius-like approach of power-series expansions. The indicial
equations restrict the set of possible leading powers to a few cases,
describing, e.g., black holes, wormholes, or naked singularities.
  We focus on the black hole case and derive recurrent formulas for all series
coefficients of the infinite power-series expansion around the horizon. The
solution is characterized by electric charge $q$, the black-hole radius $a_0$,
and the Bach parameter $b$ related to the strength of the Bach tensor at the
horizon. However, the Bach parameter has to be fine-tuned to ensure asymptotic
flatness. The fine-tuning of $b$ for a given $q$ and $a_0$ returns up to two
values, describing two branches of asymptotically flat, static, spherically
symmetric, charged black holes in quadratic gravity. This is in agreement with
previous numerical works.
  We discuss various physical properties of these black holes, such as their
asymptotic mass, temperature, photon spheres, and black-hole shadows. A
straightforward generalization to dyonic black holes in quadratic gravity is
also briefly mentioned.
